/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":63,"initialQuestionWindow":[{"id":"9d209464-7ab2-4a44-9261-7675c305b949","revisionId":"e0c8116c-b798-40cd-bb37-3f17b140ce9d","questionNumber":"15","questionType":"LA","specification":"Given that\n\n$$x + 9 : 5x - 1 = x + 7 : 2x - 3$$","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"b0ce2aea-a518-46f2-b10a-58edbff7974a","label":"0","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{x+9}{5x-1} = \\frac{x+7}{2x-3}$ M1\n- Cross multiply: $(x+9)(2x-3) = (x+7)(5x-1)$ M1\n- Expand and simplify to $3x^2 + 19x + 20 = 0$ M1\n- Solve to get $x = -4/3$ or $x = -5$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Converts ratio to an algebraic fraction equation.","code":"M"},{"id":"p2","marks":1,"description":"Cross multiplies and expands brackets correctly.","code":"M"},{"id":"p3","marks":1,"description":"Simplifies to $3x^2 + 19x + 20 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Finds both solutions $x = -4/3$ and $x = -5$.","code":"A"}],"finalAnswers":["-4/3","-5"],"generatedAt":"2026-08-10T10:27:46.399Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"c6fb4ad0-8ab4-45f7-a782-c9eb1eea9f20","revisionId":"a5a2a770-51d8-4819-b039-2ae2c0854a26","questionNumber":"16","questionType":"LA","specification":"Given that\n\n$$5 - 3x : 9 - x = 3x + 7 : 4 - x$$","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"17eed567-8186-4cb1-a800-b65dd0d3d2b9","label":"0","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{5-3x}{9-x} = \\frac{3x+7}{4-x}$ M1\n- Cross multiply: $(5-3x)(4-x) = (3x+7)(9-x)$ M1\n- Expand and simplify to $6x^2 - 37x - 43 = 0$ M1\n- Solve to get $x = 43/6$ or $x = -1$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Converts ratio to an algebraic fraction equation.","code":"M"},{"id":"p2","marks":1,"description":"Cross multiplies and expands brackets correctly.","code":"M"},{"id":"p3","marks":1,"description":"Simplifies to $6x^2 - 37x - 43 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Finds both solutions $x = 43/6$ and $x = -1$.","code":"A"}],"finalAnswers":["43/6","-1"],"generatedAt":"2026-08-10T10:27:46.399Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null}],"subjectCode":"gcse_maths","summaries":[{"id":"d09aae9a-bc4b-4819-84a5-d2f7793bd6b4","difficultyBand":"hard","calculatorUse":null},{"id":"1beaa2b3-8fba-4912-a538-851dead9b005","difficultyBand":"hard","calculatorUse":null},{"id":"1c8bd641-25fd-4953-bb02-81a3a0eb8d60","difficultyBand":"hard","calculatorUse":null},{"id":"317a6bef-5a53-470e-bd04-7f50a8b0cbd0","difficultyBand":"hard","calculatorUse":null},{"id":"3394cd8d-61ac-4414-8133-45ded4fcc42a","difficultyBand":"hard","calculatorUse":null},{"id":"3ddd763e-87b5-4e51-a425-e07e163b102d","difficultyBand":"hard","calculatorUse":null},{"id":"6177c304-e3d8-4302-b036-8eb7b154c279","difficultyBand":"hard","calculatorUse":null},{"id":"63f39f22-9af6-42e5-8505-b7faa2f277a8","difficultyBand":"hard","calculatorUse":null},{"id":"65038096-a2f3-4ac6-a5d9-40c46647dce0","difficultyBand":"hard","calculatorUse":null},{"id":"669d940d-3383-4891-8833-36e34a72dcb6","difficultyBand":"hard","calculatorUse":null},{"id":"9130d069-1f56-4520-b84b-3e77f3ce1ed2","difficultyBand":"hard","calculatorUse":null},{"id":"967f95d2-cfef-4cff-85d1-5f12f88b42e5","difficultyBand":"hard","calculatorUse":null},{"id":"9b191aa8-f4dd-465b-a60a-6cb2924300bb","difficultyBa

Algebraic Fractions

Question 61

Algebraic Fractions Questions

Algebraic Fractions

Question 61

Algebraic Fractions Questions