/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":55,"initialQuestionWindow":[{"id":"0904d9ed-910b-4e89-98a4-a2c0af0ce71a","revisionId":"4d3eca48-728c-451a-8ea9-c1b2befac229","questionNumber":"7","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":3,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"c2232f1d-e417-44cc-955a-8809d2f0891b","label":"0","content":"Simplify fully $\\frac{3x+6}{x-4} \\div \\frac{2x^2+9x+10}{x^2-4x}$","markscheme":"- Invert second fraction and multiply: $\\frac{3x+6}{x-4} \\times \\frac{x^2-4x}{2x^2+9x+10}$ M1\n- Factorise all terms: $\\frac{3(x+2)}{x-4} \\times \\frac{x(x-4)}{(2x+5)(x+2)}$ M1\n- Cancel common factors to get $\\frac{3x}{2x+5}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Inverts the divisor and changes to multiplication.","code":"M"},{"id":"p2","marks":1,"description":"Factorises at least two expressions correctly.","code":"M"},{"id":"p3","marks":1,"description":"Final answer $\\frac{3x}{2x+5}$.","code":"A"}],"finalAnswers":["\\frac{3x}{2x+5}"],"generatedAt":"2026-08-10T10:27:46.399Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"929ab195-159e-4cd5-969e-3111a7c595e4","revisionId":"9ec99fc7-b325-41a7-93f1-2398693e9a26","questionNumber":"8","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":3,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"5264b7b9-b053-4b0c-9c8f-13964e19c08a","label":"0","content":"Simplify fully $\\frac{2x-2}{x+5} \\div \\frac{x^2-4x+3}{2x^2+13x+15}$","markscheme":"- Invert second fraction and multiply: $\\frac{2(x-1)}{x+5} \\times \\frac{(2x+3)(x+5)}{(x-3)(x-1)}$ M1\n- Factorise all terms correctly M1\n- Cancel common factors to get $\\frac{2(2x+3)}{x-3}$ or $\\frac{4x+6}{x-3}$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Inverts the divisor and changes to multiplication.","code":"M"},{"id":"p2","marks":1,"description":"Factorises at least two expressions correctly.","code":"M"},{"id":"p3","marks":1,"description":"Final answer $\\frac{2(2x+3)}{x-3}$ or equivalent.","code":"A"}],"finalAnswers":["\\frac{2(2x+3)}{x-3}","\\frac{4x+6}{x-3}"],"generatedAt":"2026-08-10T10:27:46.399Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"51f4b4ca-8f85-491d-8c14-70ba2118f9c8","revisionId":"df3c4971-695d-412a-8383-cd31a90666d9","questionNumber":"9","questionType":"LA","specification":"","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":"Algebraic Fractions","calculatorUse":null,"parts":[{"id":"d03db4b9-496f-4723-9420-295faabb8ab4","label":"0","content":"Solve $\\frac{8}{x + 3} + \\frac{3}{x + 8} = 1$","markscheme":"- Multiply by common denominator: $8(x+8) + 3(x+3) = (x+3)(x+8)$ M1\n- Expand and simplify to quadratic: $11x + 73 = x^2 + 11x + 24$ M1\n- Rearrange to $x^2 - 49 = 0$ M1\n- Solve to get $x = 7$ or $x = -7$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Eliminates fractions by multiplying by $(x+3)(x+8)$.","code":"M"},{"id":"p2","marks":1,"description":"Expands brackets correctly to reach a quadratic form.","code":"M"},{"id":"p3","marks":1,"description":"Simplifies to $x^2 = 49$ or $x^2 - 49 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Finds both solutions $x = 7$ and $x = -7$.","code":"A"}],"finalAnswers":["7","-7"],"generatedAt":"2026-08-10T10:27:46.399Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null}],"subjectC

Algebraic Fractions

Question 53

Algebraic Fractions Questions

Algebraic Fractions

Question 53

Algebraic Fractions Questions