Simplify (qx+a)/(rx+b) +/- (sx+c)/(rx+b)^2
\nx is a randomised variable. a,b,c,d,q,r are randomised integers.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Express $\\displaystyle{\\var{te[0]}\\var{sgnl}\\var{te[1]}}$ as a single fraction.
", "advice": "\\[\\begin{align*} \\var{te[0]}\\var{sgnl}\\var{te[1]} &= \\frac{\\var{ndnde[1]}}{\\var{ndnde[1]}}\\times\\var{te[0]}\\var{sgnl}\\var{te[1]}\\\\&=\\frac{(\\var{ndnde[1]})(\\var{ndnde[0]})\\var{sgnl}(\\var{ndnde[2]})}{\\var{ndnde[3]}}\\\\&=\\frac{(\\var{cnd[0]})\\var{sgnl}(\\var{ndnde[2]})}{\\var{ndnde[3]}}\\\\&=\\var{ans} \\end{align*}\\]
\nThere is no benefit in expanding the denominator. In fact, it is best to leave the denominator factorised, because then it is easier to see if the fraction can be simplified.
\nThe next step after this would be to try to factorise the numerator, and then see if the fraction can be simplified.
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", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random([0,0,random(1,3,5),abs(rnd[0]),abs(rnd[0]),rnd[1]],\n [1,1,random(1,3,5),rnd[0],rnd[1],rnd[2] ])", "description": "the constants: num1 xc, num2 xc, den xc, num1 c, num2 c, den c
\nThey are set up so that the numerators are either the same constant, or expressions x+k, which are different to the denominator expressions; and, the terms in each denominator are coprime.
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", "templateType": "anything", "can_override": false}, "ansnum": {"name": "ansnum", "group": "Ungrouped variables", "definition": "cnd[1]", "description": "", "templateType": "anything", "can_override": false}, "ansden": {"name": "ansden", "group": "Ungrouped variables", "definition": "ndnde[3]", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "expression(\"(\"+string(ansnum)+\")/(\"+string(ansden)+\")\")", "description": "", "templateType": "anything", "can_override": false}, "rnd": {"name": "rnd", "group": "Ungrouped variables", "definition": "shuffle(-5..5 except 0)", "description": "list of distinct random numbers between -5 and 5
", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "76"}, "ungrouped_variables": ["v", "rnd", "c", "ndnd", "ndnde", "te", "sgn", "sgnl", "cnd", "ansnum", "ansden", "ans"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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": "{ans}", "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": "?`+/?`+", "partialCredit": 0, "message": "You need to give your answer as just one fraction", "nameToCompare": ""}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}