// Numbas version: exam_results_page_options
{"name": "Combining algebraic fractions 6.2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"chcp": {"definition": "if(gcd(a,d)=1,d,chcp(a,b,c,random(b..c)))", "type": "number", "language": "jme", "parameters": [["a", "number"], ["b", "number"], ["c", "number"], ["d", "number"]]}}, "name": "Combining algebraic fractions 6.2", "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "combining algebraic fractions", "common denominator"], "advice": "\n    <p>Using the information given by Show steps&nbsp;we have:</p>\n  <p>\\[\\simplify[std]{ {a} / ({a1}x + {b}) + ({c}x+{d}) /( ({a2}x + {b})^2)&nbsp;&nbsp;= ({a} * ({a1}*x + {b}) + {c}*x+{d} ) / (({a1}*x + {b})^2) = ({a*a1+c} * x + {a * b + d}) / (({a1}*x + {b})^2 )}\\]</p>\n    ", "rulesets": {"std": ["all", "fractionNumbers"]}, "parts": [{"stepspenalty": 1.0, "prompt": "<p>Express \\[\\simplify[std]{{a} / ({a1}x + {b}) + ({c}x+{d}) /( ({a2}x + {b})^2)}\\] 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>Click on Show steps if you require help. You will lose one mark if you do so.</p>\n      <p>&nbsp;</p>", "gaps": [{"notallowed": {"message": "<p>Input as a single fraction and also 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": "std", "marks": 2.0, "answer": "({a*a2+c} * x + {a * b +  d })/ (({a1}*x + {b})^2)", "type": "jme"}], "steps": [{"prompt": "\n            <p>The formula for {nb} fractions in this case is :<br/>\\[\\simplify[std]{a / b + {s1} * (c / b^2) = (ab + {s1} * c) / b^2}\\]</p>\n          <p>This is because you can choose the denominator of the single fraction to be an expression which the denominators of the separate fractions both divide into. In this case both divide into $b^2$, so best to choose this.</p>\n          <p>For this exercise we have $\\simplify{b={a1}x+{b}}$.</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.</p>\n    <p>&nbsp;</p>\n    \n    ", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(1..9)", "name": "a"}, "c": {"definition": "random(-9..9 except 0)", "name": "c"}, "b": {"definition": "chcp(a1,1,9,random(-9..9 except 0))", "name": "b"}, "d": {"definition": "random(-6..6 except[0,round(b*c/a2)])", "name": "d"}, "nb": {"definition": "if(c<0,'taking away','adding')", "name": "nb"}, "a1": {"definition": "random(1..8 except 0)", "name": "a1"}, "a2": {"definition": "a1", "name": "a2"}, "s1": {"definition": "if(c<0,-1,1)", "name": "s1"}}, "metadata": {"notes": "<p><strong>19/08/2012:</strong></p>\n    <p>Added tags.</p>\n    <p>Added description.</p>\n    <p>Modified copy of Combining algebraic fractions 1.&nbsp;</p>\n    <p>Introduced function chcp to make sure that the denominator was not of the form (ax+b) where a and b have a common factor.</p>\n    <p>Checked calculations.OK.</p>\n    <p><strong>02/02/2013:</strong></p>\n    <p>Added instructions to simplify the numerator.</p>", "description": "<p>Express $\\displaystyle \\frac{a}{x + b} +\\frac{cx+d}{(x + b)^2}$&nbsp;as an algebraic single fraction.</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/"}]}