/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":14,"initialQuestionWindow":[{"id":"b94bf307-8058-452b-bd4c-8fc0902c992e","revisionId":"42462ef1-72db-4ea5-936c-d709d84f4f14","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"408fa863-95e0-486c-806c-1e376bcf2682","label":null,"content":"Simplify fully $\\frac{x + 5}{x^2 - 25}$","markscheme":"- Factorise denominator: $\\frac{x+5}{(x+5)(x-5)}$ M1\n- Simplify by cancelling $(x+5)$ to get $\\frac{1}{x-5}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Factorises the denominator as the difference of two squares $(x+5)(x-5)$","code":"M"},{"id":"p2","marks":1,"description":"Cancels the common factor to obtain the final simplified fraction","code":"A"}],"finalAnswers":["\\frac{1}{x-5}"],"generatedAt":"2026-08-10T10:38:21.779Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"e8bb013f-cc6e-45fc-ba2c-bbb663d9efad","revisionId":"2ba3b61a-aaea-4cbb-8a65-74d5d8212689","questionNumber":null,"questionType":"LA","specification":"Given that\n\n$$2x + 1 : x + 2 = 5x - 3 : 2x$$","difficulty":3,"difficultyBand":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"8d373728-0e2d-4af4-be18-f235fb290b75","label":"a","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{2x+1}{x+2} = \\frac{5x-3}{2x}$ M1\n- Cross multiply: $2x(2x+1) = (x+2)(5x-3)$ M1\n- Expand and simplify to $x^2 + 5x - 6 = 0$ M1\n- Solve to get $x = 1$ or $x = -6$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Sets up the initial equation from the ratio: $\\frac{2x+1}{x+2} = \\frac{5x-3}{2x}$","code":"M"},{"id":"p2","marks":1,"description":"Correctly cross multiplies the algebraic fractions: $2x(2x+1) = (x+2)(5x-3)$","code":"M"},{"id":"p3","marks":1,"description":"Expands brackets and simplifies the expression to reach a standard quadratic equation $x^2 + 5x - 6 = 0$","code":"M"},{"id":"p4","marks":1,"description":"Solves the quadratic equation to find two correct values for $x$.","code":"A"}],"finalAnswers":["x = 1, x = -6","1, -6"],"generatedAt":"2026-08-10T10:38:46.554Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"eb8c3fb7-4cda-4302-aee4-5a4b3c276305","revisionId":"691dc30b-746b-4ffa-bb1c-d5e27816df02","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"a152a78d-fc6f-48be-8e02-998648c8d840","label":"a","content":"Simplify fully $\\frac{x^2 + 3x}{x^2 + 8x + 15}$","markscheme":"- Factorise numerator and denominator: $\\frac{x(x+3)}{(x+3)(x+5)}$ M1\n- Simplify by cancelling $(x+3)$ to get $\\frac{x}{x+5}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Factorise numerator and denominator: $\\frac{x(x+3)}{(x+3)(x+5)}$","code":"M"},{"id":"p2","marks":1,"description":"Simplify by cancelling $(x+3)$ to get $\\frac{x}{x+5}$","code":"A","acceptable":["x/(x+5)"]}],"finalAnswers":["\\frac{x}{x+5}"],"generatedAt":"2026-08-10T10:39:02.907Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null}],"initialQuestions":null,"initialView":"runner","intro":"$L3d","subjectCode":"gcse_maths","summaries":[{"id":"d09aae9a-bc4b-4819-84a5-d2f7793bd6b4","difficultyBand":null,"calculatorUse":null},{"id":"1beaa2b3-8fba-4912-a538-851dead9b005","difficultyBand":null,"calculatorUse":null},{"id":"1c8bd641-25fd-4

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions

Algebraic Fractions Questions