/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":60,"initialQuestionWindow":[{"id":"11bfff96-d1b5-4fb4-a5d6-f3d09a60c84b","revisionId":"dee98266-aeb2-4ea0-b860-4a20257e3fff","questionNumber":"12","questionType":"LA","specification":"","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"cd76f88a-f6af-4001-8498-1863e96f110a","label":"0","content":"Solve $\\frac{7}{x + 1} - \\frac{4}{3x - 2} = 1$","markscheme":"- Multiply by common denominator: $7(3x-2) - 4(x+1) = (x+1)(3x-2)$ M1\n- Expand and simplify: $17x - 18 = 3x^2 + x - 2$ M1\n- Rearrange to $3x^2 - 16x + 16 = 0$ M1\n- Factorise $(3x-4)(x-4) = 0$ to get $x = 4/3$ or $x = 4$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Eliminates fractions by multiplying by $(x+1)(3x-2)$.","code":"M"},{"id":"p2","marks":1,"description":"Expands and simplifies to a quadratic equation.","code":"M"},{"id":"p3","marks":1,"description":"Simplifies to $3x^2 - 16x + 16 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Finds both solutions $x = 4/3$ and $x = 4$.","code":"A"}],"finalAnswers":["4/3","4"],"generatedAt":"2026-08-10T10:27:46.399Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"8aefa908-c49d-46a2-9247-dd02c0e50f95","revisionId":"6a321364-ca4c-40f9-acff-b6a525993fbf","questionNumber":"13","questionType":"LA","specification":"Given that\n\n$$2x + 1 : x + 2 = x + 8 : 3x - 4$$","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"5e2d77f2-09ec-4a9f-97e1-797210041f20","label":"0","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{2x+1}{x+2} = \\frac{x+8}{3x-4}$ M1\n- Cross multiply: $(2x+1)(3x-4) = (x+8)(x+2)$ M1\n- Expand and simplify to $x^2 - 3x - 4 = 0$ M1\n- Solve to get $x = 4$ 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 $x^2 - 3x - 4 = 0$ or equivalent.","code":"M"},{"id":"p4","marks":1,"description":"Finds both solutions $x = 4$ and $x = -1$.","code":"A"}],"finalAnswers":["4","-1"],"generatedAt":"2026-08-10T10:27:46.399Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"848156c2-c256-4f6f-8b89-af3f2ab121dd","revisionId":"b0494f19-9c06-4a4a-b6b0-70305c8018dc","questionNumber":"14","questionType":"LA","specification":"Given that\n\n$$x - 1 : 2x - 3 = x + 2 : 3x - 2$$","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"52d2ef47-dc1d-4f9a-be68-1d4f9716216a","label":"0","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{x-1}{2x-3} = \\frac{x+2}{3x-2}$ M1\n- Cross multiply: $(x-1)(3x-2) = (x+2)(2x-3)$ M1\n- Expand and simplify to $x^2 - 6x + 8 = 0$ M1\n- Solve to get $x = 2$ or $x = 4$ 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 $x^2 - 6x + 8 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Finds both solutions $x = 2$ and $x = 4$.","code":"A"}],"finalAnswers":["2","4"],"generatedAt":"2026-08-10T10:27:46.399Z","mo

Algebraic Fractions

Question 58

Algebraic Fractions Questions

Algebraic Fractions

Question 58

Algebraic Fractions Questions