// Numbas version: finer_feedback_settings
{"name": "Combining algebraic fractions 6.3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Combining algebraic fractions 6.3", "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "combining algebraic fractions", "common denominator"], "advice": "\n    <p>Show steps tells us that a good choice for the denominator of the algebraic fraction we are looking for is &nbsp;$\\simplify{(x+{p})({a1}x+{b})({a2}x+{d})}$.</p>\n    <p>Hence we have:<br/>\\[\\begin{eqnarray*} \\simplify{{a} /((x+{p}) ({a1}x + {b})) + ({c} /( (x+{p})({a2}x + {d})))}&nbsp;&nbsp;&amp;=&amp; \\simplify[std]{({a} * ({a2}*x + {d}) + {c} * ({a1}*x + {b})) / ((x+{p})({a1}*x + {b}) * ({a2}*x + {d})) }\\\\&amp;=&amp; \\simplify{({a*a2 + c*a1} * x + {a * d + c * b}) / ((x+{p})({a1}*x + {b}) * ({a2}*x + {d}))}\\end{eqnarray*}\\]</p>\n    ", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"], "std1": ["std", "collectNumbers"]}, "parts": [{"stepspenalty": 1.0, "prompt": "<p>Express \\[\\simplify{{a} /((x+{p}) ({a1}x + {b})) + ({c} /( (x+{p})({a2}x + {d})))}\\] as a single fraction.</p>\n      <p>Input the fraction here: [[0]].</p>\n      <p>Make sure that you simplify the numerator.</p>\n      <p>&nbsp;Click on Show steps if you need help. You will lose one mark of you do so.</p>", "gaps": [{"notallowed": {"message": "<p>Input as a single fraction and make sure that you simplify the numerator.</p>", "showstrings": false, "strings": [")-", ")+"], "partialcredit": 0.0}, "checkingaccuracy": 1e-05, "vsetrange": [10.0, 11.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std1", "marks": 2.0, "answer": "({a*a2 +  c*a1} * x + {a * d +  c * b})/ ((x+{p})({a1}*x + {b}) * ({a2}*x + {d}))", "type": "jme"}], "steps": [{"prompt": "\n            <p>Note that the denominators both have the factor $\\simplify{x+{p}}$ hence we see that a common denominator is $\\simplify{(x+{p})({a1}x+{b})({a2}x+{d})}$ as both denominators, $\\simplify{(x+{p})({a1}x+{b})}$ and&nbsp;&nbsp;$\\simplify{(x+{p})({a2}x+{d})}$,&nbsp;divide into it.</p>\n            <p>Note that in your answer you do not need to expand the denominator.</p>\n            ", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "extensions": [], "statement": "\n    <p>Add the following two fractions together and express as a single fraction over a common denominator.</p>\n    <p>&nbsp;</p>\n    \n    ", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(2..9)", "name": "a"}, "c": {"definition": "random(-9..9 except 0)", "name": "c"}, "b": {"definition": "random(-9..9 except 0)", "name": "b"}, "d": {"definition": "random(-9..9 except [0,round(b*a2/a1)])", "name": "d"}, "nb": {"definition": "if(c<0,'taking away','adding')", "name": "nb"}, "a1": {"definition": "random(1..8)", "name": "a1"}, "p": {"definition": "random(-9..9 except [round(b/a1),round(d/a2)])", "name": "p"}, "a2": {"definition": "random(1..8)", "name": "a2"}, "s1": {"definition": "if(c<0,-1,1)", "name": "s1"}}, "metadata": {"notes": "<p><strong>5/08/2012:</strong></p>\n    <p>Added tags.</p>\n    <p>Added description.</p>\n    <p>Changed to two questions, for the numerator and denomimator, rather than one as difficult to trap student input for this example. Still some ambiguity however.</p>\n    <p><strong>12/08/2012:</strong></p>\n    <p>Back to one input of a fraction and trapped input in Forbidden Strings.</p>\n    <p>Used the except feature of ranges to get non-degenerate examples.</p>\n    <p>Checked calculation.OK.</p>\n    <p>Improved display in content areas.</p>\n    <p><strong>02/02/2013:</strong></p>\n    <p>Added instructions to simplify the numerator.</p>", "description": "<p>Express $\\displaystyle \\frac{a}{(x+r)(px + b)} + \\frac{c}{(x+r)(qx + d)}$&nbsp;as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}