// Numbas version: finer_feedback_settings
{"name": "Line\u00e6re likninger (f\u00f8rstegradslikninger)", "metadata": {"description": "<p>&Oslash;ving i &aring; l&oslash;se line&aelig;re likninger. L&oslash;sninger angis som heltall eller br&oslash;k.</p>", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Line\u00e6re likninger", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", ""], "variable_overrides": [[], []], "questions": [{"name": "Line\u00e6re likninger 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Torris Bakke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/942/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}], "tags": [], "metadata": {"description": "<p>Solve linear equations with one unknown. Including brackets and fractions.</p>", "licence": "None specified"}, "statement": "<p>L&oslash;s likningene. Oppgi svarene som heltall eller br&oslash;k.</p>", "advice": "<h3><strong>Oppgave a)</strong></h3>\n<p>\\[\\simplify{{a}x+{b} = {c}} \\]</p>\n<p>F&oslash;rst samler vi alle&nbsp; $x$-leddene p&aring; den ene siden av likningen.</p>\n<p>For &aring; f&aring; det til m&aring; vi {add[0]} $\\var{abs(b)}$ {add[1]} begge sider:</p>\n<p>\\[\\simplify[all,!collectNumbers]{{a}x+{b} - {b} = {c} - {b}}&nbsp;\\]</p>\n<p>\\[\\var{a}x &nbsp;= \\simplify{{c-b}} \\]</p>\n<p>For &aring; f&aring; $x$ alene deler vi p&aring; koeffisienten til $x$ (tallet foran $x$) p&aring; begge sider.</p>\n<p>Vi deler p&aring; $\\var{a}$:</p>\n<p>\\[ &nbsp;x = {\\simplify{({c}-{b})/{a}}} \\]</p>\n<p></p>\n<h3><strong>Oppgave b)</strong></h3>\n<p>&nbsp;\\[ \\frac{\\simplify{{d}x + {f}}}{\\var{g}} = \\var{h} \\]<br/><br/>F&oslash;rst vil vi kvitte oss med br&oslash;ken p&aring; venstre side. &nbsp;Det gj&oslash;r vi ved &aring; multiplisere begge sidene med $\\var{g}$:<br/><br/>\\[ \\begin{split} \\frac{\\simplify{{d}x + {f}}}{\\var{g}} \\cdot \\var{g}&nbsp; &amp;= \\var{h} \\cdot \\var{g} \\\\\\\\ \\simplify{{d}x + {f}} &amp;= \\var{h*g} \\end{split} \\]<br/><br/>Det neste vi gj&oslash;r er &aring; samle $x$-leddene p&aring; den ene siden av likningen.<br/><br/>Vi m&aring; da {add2[0]} $\\var{abs(f)}$ {add2[1]} begge sider:<br/><br/>\\[ \\begin{split}&nbsp;\\var{d}x &amp;= \\simplify[]{{h*g}-{f}} \\\\ &amp;= \\simplify[]{{h*g-f}} \\end{split}\\]<br/><br/>Til slutt m&aring; vi dele p&aring; $\\var{d}$ for &aring; f&aring; $x$ alene p&aring; venstre siden.</p>\n<p><br/>\\[x = \\simplify[fractionNumbers]{{(h*g-f)/d}} &nbsp;\\]</p>\n<p></p>\n<h3>Oppgave c)</h3>\n<p>\\[ \\simplify{{b}({c}x+{g})} = \\var{d} \\]</p>\n<p>I oppgave b) var $x$-uttrykket delt p&aring; $\\var{g}$, og vi m&aring;tte da multiplisere for &aring; f&aring; bort nevneren.&nbsp; Her er $x$-uttrykket multiplisert med et tall, og da m&aring; vi dividere for &aring; bli kvitt det-<br/>Vi deler begge sider p&aring; $\\var{b}$:<br/><br/>\\[ \\begin{split} \\frac{\\simplify{{b}({c}x+{g})}}{ \\var{b}} &amp;= \\frac{\\var{d}}{\\var{b}} \\\\ \\\\ \\simplify{{c}x+{g}} &amp;= \\simplify[fractionNumbers]{{d/b}} \\end{split} \\]<br/><br/><br/>Det neste vi gj&oslash;r er &aring; samle $x$-leddene p&aring; den ene siden av likningen.<br/><br/>Vi m&aring; da {add3[0]} $\\var{abs(g)}$ {add3[1]} begge sider:</p>\n<p>\\[ \\begin {split} \\simplify[all,!collectNumbers]{{c}x + {g} - {g}} &amp;= \\simplify[fractionNumbers,!cancelTerms]{{d/b} - {g}}\\\\ \\var{c}x &amp;= \\simplify[fractionNumbers]{{d/b-g}} \\end{split} \\]<br/><br/>Til slutt m&aring; vi dele p&aring; $\\var{c}$for &aring; f&aring; $x$ alene p&aring; venstre siden.<br/>\\[ x = &nbsp;\\simplify[fractionNumbers]{{(d/b-g)/c}} \\]</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-20..20 except 0 except 1 except -1)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-20..20 except [0,1,-1])", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-20..20 except [-1,0,1])", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-20..20 except 0 except 1 except -1)", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(-20..20 except 0)", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random(-20..20 except 0 except 1 except -1)", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(-20..20 except 0)", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(-20..20 except 0)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(-20..20 except 0)", "description": "", "templateType": "anything", "can_override": false}, "add": {"name": "add", "group": "Ungrouped variables", "definition": "if (b>0,['trekke fra','p\u00e5'],['legge til','p\u00e5'])", "description": "", "templateType": "anything", "can_override": false}, "add2": {"name": "add2", "group": "Ungrouped variables", "definition": "if(f>0,['trekke fra','p\u00e5'],['legge til','p\u00e5'])", "description": "", "templateType": "anything", "can_override": false}, "add3": {"name": "add3", "group": "Ungrouped variables", "definition": "if(g>0,['trekke fra','p\u00e5'],['legge til','p\u00e5'])", "description": "", "templateType": "anything", "can_override": false}, "add3sym": {"name": "add3sym", "group": "Ungrouped variables", "definition": "if(add3='add',' + ',' - ')", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "((c-b)/a)", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "((h*g - f)/d)", "description": "", "templateType": "anything", "can_override": false}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "(((d/b) - g)/c)", "description": "", "templateType": "anything", "can_override": false}, "a4": {"name": "a4", "group": "Ungrouped variables", "definition": "(f-c)/(h-m)", "description": "", "templateType": "anything", "can_override": false}, "a5": {"name": "a5", "group": "Ungrouped variables", "definition": "((g*m-n*f)/(n*b-g*c))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "m", "n", "add", "add2", "add3", "add3sym", "a1", "a2", "a3", "a4", "a5"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{a}x+{b} = {c}}$</p>\n<p></p>\n<p>$x=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, 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"suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\dfrac{\\simplify{{d}x + {f}}}{\\var{g}} = \\var{h}$</p>\n<p></p>\n<p>$x=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a2}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "`+-rational:$n", "partialCredit": 0, "message": "", "nameToCompare": "", "warningTime": "submission"}, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{b}({c}x+{g})} = \\var{d}$</p>\n<p></p>\n<p>$x=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a3}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "`+-rational:$n", "partialCredit": 0, "message": "", "nameToCompare": "", "warningTime": "submission"}, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Line\u00e6re likninger 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Torris Bakke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/942/"}, {"name": "heike hoffmann", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2960/"}, {"name": "sean hunte", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3167/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}], "tags": [], "metadata": {"description": "<p>Solve linear equations with unkowns on both sides. Including brackets and fractions.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>L&oslash;s likningene. Oppgi svaret som et helt tall eller en br&oslash;k.</p>", "advice": "<p><strong>Oppgave a)</strong></p>\n<p>I $\\simplify{{l}({m}w-{n}) = {p}w+{q}}$, m&aring; vi f&oslash;rst l&oslash;se opp parentesene, deretter samler vi alle $w$'ene p&aring; venstre side og alle tallene p&aring; h&oslash;yre side. Til slutt deler vi p&aring; tallet foran $w$ (koeffisienten til $w$) for &aring; f&aring; $w$ alene.</p>\n<p></p>\n<table style=\"height: 342px; width: 813px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 249.391px;\">$\\simplify{{l}({m}w-{n})}$</td>\n<td style=\"height: 18px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">$\\simplify{{p}w+{q}}$&nbsp;</td>\n<td style=\"text-align: left; width: 185.922px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 249.391px;\">&nbsp;</td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\"></td>\n<td style=\"text-align: left; width: 185.922px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 249.391px;\">$\\simplify{{l*m}w-{n*l}}$</td>\n<td style=\"height: 18px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">$\\simplify{{p}w+{q}}$</td>\n<td style=\"text-align: left; width: 185.922px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 249.391px;\">&nbsp;</td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\"></td>\n<td style=\"text-align: left; width: 185.922px;\"></td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"text-align: right; height: 36px; width: 249.391px;\">$\\simplify[!cancelTerms,unitFactor]{{l*m}w-{n*l}-{p}w}$</td>\n<td style=\"height: 36px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 36px; width: 283.422px;\">$\\simplify[!cancelTerms,unitFactor]{{p}w+{q}-{p}w}$</td>\n<td style=\"text-align: left; width: 185.922px;\">(trekker fra $\\var{p}w$ p&aring; begge sider)</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 249.391px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">&nbsp;</td>\n<td style=\"text-align: left; width: 185.922px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 249.391px;\">$\\simplify{{l*m-p}w-{n*l}}$</td>\n<td style=\"height: 18px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">$\\var{q}$</td>\n<td style=\"text-align: left; width: 185.922px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 249.391px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">&nbsp;</td>\n<td style=\"text-align: left; width: 185.922px;\"></td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"text-align: right; height: 36px; width: 249.391px;\">$\\var{l*m-p}w-\\var{n*l}+\\var{n*l}$</td>\n<td style=\"height: 36px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 36px; width: 283.422px;\">$\\var{q}+\\var{n*l}$</td>\n<td style=\"text-align: left; width: 185.922px;\">(legger til $\\var{n*l}$ p&aring; begge sider)</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 249.391px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">&nbsp;</td>\n<td style=\"text-align: left; width: 185.922px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 249.391px;\">$\\var{l*m-p}w$</td>\n<td style=\"height: 18px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">$\\var{q+n*l}$</td>\n<td style=\"text-align: left; width: 185.922px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 249.391px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">&nbsp;</td>\n<td style=\"text-align: left; width: 185.922px;\"></td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"text-align: right; height: 36px; width: 249.391px;\">$\\displaystyle{\\frac{\\var{l*m-p}w}{\\var{l*m-p}}}$</td>\n<td style=\"height: 36px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 36px; width: 283.422px;\">$\\displaystyle{\\frac{\\var{q+n*l}}{\\var{l*m-p}}}$</td>\n<td style=\"text-align: left; width: 185.922px;\">(deler p&aring; $\\var{l*m-p}$ p&aring; begge sider)</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 249.391px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">&nbsp;</td>\n<td style=\"text-align: left; width: 185.922px;\"></td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"text-align: right; height: 36px; width: 249.391px;\">$w$</td>\n<td style=\"height: 36px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 36px; width: 283.422px;\">$\\displaystyle{\\simplify{{q+n*l}/{l*m-p}}} $</td>\n<td style=\"text-align: left; width: 185.922px;\"></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p><strong>Oppgave b)</strong></p>\n<p>I uttrykket $\\displaystyle{\\frac{\\var{d}y}{y-\\var{f}}}=\\var{g}$ m&aring; vi multiplisere med $(y-\\var{f})$ for &aring; bli kvitt br&oslash;ken, deretter f&aring;r vi alle $y$'ene p&aring; ene siden og tallene p&aring; andre siden, og til slutt deler vi p&aring; koeffisienten til $y$ for &aring; f&aring; $y$ alene..</p>\n<p></p>\n<table style=\"width: 1209px; height: 252px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; width: 382.891px; height: 18px;\">$\\displaystyle{\\frac{\\var{d}y}{y-\\var{f}}}$</td>\n<td style=\"width: 38.9688px; height: 18px;\">$=$</td>\n<td style=\"text-align: left; width: 372.938px; height: 18px;\">$\\var{g}$&nbsp;</td>\n<td style=\"text-align: left; width: 349.203px; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; width: 382.891px; height: 18px;\">&nbsp;</td>\n<td style=\"width: 38.9688px; height: 18px;\"></td>\n<td style=\"text-align: left; width: 372.938px; height: 18px;\"></td>\n<td style=\"text-align: left; width: 349.203px; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"text-align: right; width: 382.891px; height: 36px;\">$\\displaystyle{\\frac{\\var{d}y}{y-\\var{f}}}\\cdot(y-\\var{f})$</td>\n<td style=\"width: 38.9688px; height: 36px;\">$=$</td>\n<td style=\"text-align: left; width: 372.938px; height: 36px;\">$\\var{g}\\cdot (y-\\var{f})$</td>\n<td style=\"text-align: left; width: 349.203px; height: 36px;\">(multipliserer med (y-\\var{f}) )</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; width: 382.891px; height: 18px;\">&nbsp;</td>\n<td style=\"width: 38.9688px; height: 18px;\"></td>\n<td style=\"text-align: left; width: 372.938px; height: 18px;\"></td>\n<td style=\"text-align: left; width: 349.203px; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; width: 382.891px; height: 18px;\">$\\var{d}y$</td>\n<td style=\"width: 38.9688px; height: 18px;\">$=$</td>\n<td style=\"text-align: left; width: 372.938px; height: 18px;\">$\\simplify[unitFactor]{{g}y+{-g*f}}$</td>\n<td style=\"text-align: left; width: 349.203px; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; width: 382.891px; height: 18px;\"></td>\n<td style=\"width: 38.9688px; height: 18px;\"></td>\n<td style=\"text-align: left; width: 372.938px; height: 18px;\">&nbsp;</td>\n<td style=\"text-align: left; width: 349.203px; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; width: 382.891px; height: 18px;\">$\\simplify[!cancelTerms,unitFactor]{{d}y+{-g}y}$&nbsp;</td>\n<td style=\"width: 38.9688px; height: 18px;\">$=$</td>\n<td style=\"text-align: left; width: 372.938px; height: 18px;\">$\\simplify[!cancelTerms,unitFactor]{{-g*f}}$</td>\n<td style=\"text-align: left; width: 349.203px; height: 18px;\">(legger til $\\simplify{{-g}y}$ p&aring; begge sider</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; width: 382.891px; height: 18px;\"></td>\n<td style=\"width: 38.9688px; height: 18px;\"></td>\n<td style=\"text-align: left; width: 372.938px; height: 18px;\">&nbsp;</td>\n<td style=\"text-align: left; width: 349.203px; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; width: 382.891px; height: 18px;\">$\\var{d-g}y$</td>\n<td style=\"width: 38.9688px; height: 18px;\">$=$</td>\n<td style=\"text-align: left; width: 372.938px; height: 18px;\">$\\var{-g*f}$</td>\n<td style=\"text-align: left; width: 349.203px; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; width: 382.891px; height: 18px;\"></td>\n<td style=\"width: 38.9688px; height: 18px;\"></td>\n<td style=\"text-align: left; width: 372.938px; height: 18px;\">&nbsp;</td>\n<td style=\"text-align: left; width: 349.203px; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; width: 382.891px; height: 18px;\">$\\displaystyle{\\frac{\\var{d-g}y}{\\var{d-g}}}$</td>\n<td style=\"width: 38.9688px; height: 18px;\">$=$</td>\n<td style=\"text-align: left; width: 372.938px; height: 18px;\">$\\displaystyle{\\frac{\\var{-g*f}}{\\var{d-g}}}$</td>\n<td style=\"text-align: left; width: 349.203px; height: 18px;\">(deler p&aring; $\\var{d-g}$ p&aring; begge sider)</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; width: 382.891px; height: 18px;\"></td>\n<td style=\"width: 38.9688px; height: 18px;\"></td>\n<td style=\"text-align: left; width: 372.938px; height: 18px;\">&nbsp;</td>\n<td style=\"text-align: left; width: 349.203px; height: 18px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; width: 382.891px; height: 18px;\">&nbsp;$y$</td>\n<td style=\"width: 38.9688px; height: 18px;\">$=$</td>\n<td style=\"text-align: left; width: 372.938px; height: 18px;\">$\\displaystyle{\\simplify{{-g*f}/{d-g}}}$</td>\n<td style=\"text-align: left; width: 349.203px; height: 18px;\"></td>\n</tr>\n</tbody>\n</table>\n<p><strong>Oppgave c)</strong></p>\n<p>I uttrykket $\\displaystyle{\\frac{x+\\var{add}}{\\var{denom1}}+\\frac{x}{\\var{denom2}}=\\var{right}}$ m&aring; vi multiplisere begge sider med $\\var{denom1}$ og by $\\var{denom2}$ for &aring; bli kvitt alle br&oslash;kene, deretter f&aring;r vi alle $x$'ene p&aring; ene siden og tallene p&aring; andre siden,og til slutt deler vi begge sidene p&aring; koeffisienten til $x$ for &aring; f&aring; $x$ alene.</p>\n<p></p>\n<table style=\"height: 403px;\">\n<tbody>\n<tr style=\"height: 34px;\">\n<td style=\"text-align: right; height: 34px; width: 565.122314453125px;\">$\\displaystyle{\\frac{x+\\var{add}}{\\var{denom1}}+\\frac{x}{\\var{denom2}}}$</td>\n<td style=\"height: 34px; width: 29.076087951660156px;\">$=$</td>\n<td style=\"text-align: left; height: 34px; width: 341.98370361328125px;\">$\\var{right}$&nbsp;</td>\n<td style=\"text-align: left; height: 34px; width: 126.83424377441406px;\"></td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"text-align: right; height: 17px; width: 565.122314453125px;\">&nbsp;</td>\n<td style=\"height: 17px; width: 29.076087951660156px;\"></td>\n<td style=\"text-align: left; height: 17px; width: 341.98370361328125px;\"></td>\n<td style=\"text-align: left; height: 17px; width: 126.83424377441406px;\"></td>\n</tr>\n<tr style=\"height: 52px;\">\n<td style=\"text-align: right; height: 52px; width: 565.122314453125px;\">$\\displaystyle{\\left(\\frac{x+\\var{add}}{\\var{denom1}}\\right)\\cdot\\var{denom1}+\\left(\\frac{x}{\\var{denom2}}\\right)\\cdot\\var{denom1}}$</td>\n<td style=\"height: 52px; width: 29.076087951660156px;\">$=$</td>\n<td style=\"text-align: left; height: 52px; width: 341.98370361328125px;\">$\\var{right}\\cdot \\var{denom1}$</td>\n<td style=\"text-align: left; height: 52px; width: 126.83424377441406px;\">(multipliserer alle ledd med $\\var{denom1}$)</td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"text-align: right; height: 17px; width: 565.122314453125px;\">&nbsp;</td>\n<td style=\"height: 17px; width: 29.076087951660156px;\"></td>\n<td style=\"text-align: left; height: 17px; width: 341.98370361328125px;\"></td>\n<td style=\"text-align: left; height: 17px; width: 126.83424377441406px;\"></td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"text-align: right; height: 17px; width: 565.122314453125px;\">$\\displaystyle{x+\\var{add}+\\frac{\\var{denom1}x}{\\var{denom2}}}$</td>\n<td style=\"height: 17px; width: 29.076087951660156px;\">$=$</td>\n<td style=\"text-align: left; height: 17px; width: 341.98370361328125px;\">$\\var{r1}$</td>\n<td style=\"text-align: left; height: 17px; width: 126.83424377441406px;\"></td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"text-align: right; height: 17px; width: 565.122314453125px;\"></td>\n<td style=\"height: 17px; width: 29.076087951660156px;\"></td>\n<td style=\"text-align: left; height: 17px; width: 341.98370361328125px;\">&nbsp;</td>\n<td style=\"text-align: left; height: 17px; width: 126.83424377441406px;\"></td>\n</tr>\n<tr style=\"height: 52px;\">\n<td style=\"text-align: right; height: 52px; width: 565.122314453125px;\">$\\displaystyle{(x+\\var{add})\\cdot\\var{denom2}+\\left(\\frac{\\var{denom1}x}{\\var{denom2}}\\right)\\cdot\\var{denom2}}$&nbsp;</td>\n<td style=\"height: 52px; width: 29.076087951660156px;\">$=$</td>\n<td style=\"text-align: left; height: 52px; width: 341.98370361328125px;\">$\\var{r1}\\cdot\\var{denom2}$</td>\n<td style=\"text-align: left; height: 52px; width: 126.83424377441406px;\">(multipliserer alle ledd med $\\var{denom2}$)</td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"text-align: right; height: 17px; width: 565.122314453125px;\"></td>\n<td style=\"height: 17px; width: 29.076087951660156px;\"></td>\n<td style=\"text-align: left; height: 17px; width: 341.98370361328125px;\">&nbsp;</td>\n<td style=\"text-align: left; height: 17px; width: 126.83424377441406px;\"></td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"text-align: right; height: 17px; width: 565.122314453125px;\">$\\displaystyle{\\var{denom2}x+\\var{a2}+\\var{denom1}x}$</td>\n<td style=\"height: 17px; width: 29.076087951660156px;\">$=$</td>\n<td style=\"text-align: left; height: 17px; width: 341.98370361328125px;\">$\\var{r12}$</td>\n<td style=\"text-align: left; height: 17px; width: 126.83424377441406px;\"></td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"text-align: right; height: 17px; width: 565.122314453125px;\"></td>\n<td style=\"height: 17px; width: 29.076087951660156px;\"></td>\n<td style=\"text-align: left; height: 17px; width: 341.98370361328125px;\">&nbsp;</td>\n<td style=\"text-align: left; height: 17px; width: 126.83424377441406px;\"></td>\n</tr>\n<tr style=\"height: 34px;\">\n<td style=\"text-align: right; height: 34px; width: 565.122314453125px;\">$\\var{sumdeno}x+\\var{a2}$</td>\n<td style=\"height: 34px; width: 29.076087951660156px;\">$=$</td>\n<td style=\"text-align: left; height: 34px; width: 341.98370361328125px;\">$\\var{r12}$</td>\n<td style=\"text-align: left; height: 34px; width: 126.83424377441406px;\">(samler ledd av samme type)</td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"text-align: right; height: 17px; width: 565.122314453125px;\"></td>\n<td style=\"height: 17px; width: 29.076087951660156px;\"></td>\n<td style=\"text-align: left; height: 17px; width: 341.98370361328125px;\">&nbsp;</td>\n<td style=\"text-align: left; height: 17px; width: 126.83424377441406px;\"></td>\n</tr>\n<tr style=\"height: 34px;\">\n<td style=\"text-align: right; height: 34px; width: 565.122314453125px;\">&nbsp;$\\var{sumdeno}x$</td>\n<td style=\"height: 34px; width: 29.076087951660156px;\">$=$</td>\n<td style=\"text-align: left; height: 34px; width: 341.98370361328125px;\">$\\var{r12}-\\var{a2}$</td>\n<td style=\"text-align: left; height: 34px; width: 126.83424377441406px;\">(samler ledd av samme type)</td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"text-align: right; height: 17px; width: 565.122314453125px;\"></td>\n<td style=\"height: 17px; width: 29.076087951660156px;\">&nbsp;</td>\n<td style=\"text-align: left; height: 17px; width: 341.98370361328125px;\"></td>\n<td style=\"text-align: left; height: 17px; width: 126.83424377441406px;\"></td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"text-align: right; height: 17px; width: 565.122314453125px;\">$\\var{sumdeno}x$</td>\n<td style=\"height: 17px; width: 29.076087951660156px;\">$=$</td>\n<td style=\"text-align: left; height: 17px; width: 341.98370361328125px;\">$\\var{top}$</td>\n<td style=\"text-align: left; height: 17px; width: 126.83424377441406px;\"></td>\n</tr>\n<tr style=\"height: 17px;\">\n<td style=\"text-align: right; height: 17px; width: 565.122314453125px;\"></td>\n<td style=\"height: 17px; width: 29.076087951660156px;\"></td>\n<td style=\"text-align: left; height: 17px; width: 341.98370361328125px;\">&nbsp;</td>\n<td style=\"text-align: left; height: 17px; width: 126.83424377441406px;\"></td>\n</tr>\n<tr style=\"height: 34px;\">\n<td style=\"text-align: right; height: 10px; width: 565.122314453125px;\">$x$</td>\n<td style=\"height: 10px; width: 29.076087951660156px;\">$=$</td>\n<td style=\"text-align: left; height: 10px; width: 341.98370361328125px;\">$\\displaystyle{\\simplify{{top}/({sumdeno})}} $</td>\n<td style=\"text-align: left; height: 10px; width: 126.83424377441406px;\">(deler med koeffisienten til $x$)</td>\n</tr>\n</tbody>\n</table>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], 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