l,"questionType":"LA","specification":"Given that\n\n$$2x + 2 : x + 3 = x + 1 : x - 1$$","difficulty":3,"difficultyBand":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"e4649d8d-ea48-4378-8374-d1e95e78b53a","label":"a","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{2x+2}{x+3} = \\frac{x+1}{x-1}$ M1\n- Cross multiply: $(2x+2)(x-1) = (x+1)(x+3)$ M1\n- Expand and simplify to $x^2 - 4x - 5 = 0$ M1\n- Solve to get $x = 5$ or $x = -1$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Sets up the equation as a ratio of fractions: $\\frac{2x+2}{x+3} = \\frac{x+1}{x-1}$","code":"M"},{"id":"p2","marks":1,"description":"Correctly cross-multiplies to get $(2x+2)(x-1) = (x+1)(x+3)$ or equivalent.","code":"M"},{"id":"p3","marks":1,"description":"Expands both sides and simplifies to a standard quadratic form, e.g., $x^2 - 4x - 5 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Solves the quadratic correctly to find both values of $x$.","code":"A"}],"finalAnswers":["x = 5, x = -1","x = 5 and x = -1"],"generatedAt":"2026-08-10T10:37:04.260Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"6177c304-e3d8-4302-b036-8eb7b154c279","revisionId":"cf35a5a8-de94-4aff-bab6-43af7041c8d8","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"27cbcf5a-54cb-417f-ae38-9e7de21a0c64","label":"a","content":"Solve $\\frac{1}{x - 1} + \\frac{12}{2x + 3} = 3$","markscheme":"- Multiply by common denominator: $1(2x + 3) + 12(x - 1) = 3(x - 1)(2x + 3)$ M1\n- Expand and simplify: $14x - 9 = 6x^2 + 3x - 9$ M1\n- Rearrange to $6x^2 - 11x = 0$ M1\n- Factorise $x(6x - 11) = 0$ to get $x = 0$ or $x = \\frac{11}{6}$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Multiply the entire equation by the common denominator $(x-1)(2x+3)$ or equate the numerators over a common denominator.","code":"M"},{"id":"p2","marks":1,"description":"Expand brackets and simplify both sides of the equation.","code":"M"},{"id":"p3","marks":1,"description":"Rearrange the equation into a standard quadratic form $ax^2 + bx + c = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Solve the quadratic equation to find both values of $x$.","code":"A"}],"finalAnswers":["x = 0, x = \\frac{11}{6}","0, 1.83"],"generatedAt":"2026-08-10T10:36:33.482Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"63f39f22-9af6-42e5-8505-b7faa2f277a8","revisionId":"ffe7009b-8f80-4817-8c4c-293e569dafbd","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"bd0090e3-cdd0-4ba8-816e-0caff76644df","label":"a","content":"Solve $\\frac{1}{x - 2} + \\frac{4}{x + 1} = 1$","markscheme":"- Multiply by common denominator: $1(x + 1) + 4(x - 2) = (x - 2)(x + 1)$ M1\n- Expand and simplify to quadratic: $5x - 7 = x^2 - x - 2$ M1\n- Rearrange to $x^2 - 6x + 5 = 0$ M1\n- Solve to get $x = 1$ or $x = 5$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Multiply both sides by the common denominator $(x - 2)(x + 1)$ correctly.","code":"M"},{"id":"p2","marks":1,"description":"Expand brackets and simplify both sides of the equation to reach a quadratic stage.","code":"M"},{"id":"p3","marks":1,"description":"Rearrange the equation into the standard quadratic form $x^2 - 6x + 5 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Solve the quadratic equation to find $x = 1$ and $x = 5$.","code":"A"}],"finalAnswers":["x = 1

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions