/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":30,"initialQuestionWindow":[{"id":"b18333d6-b072-4f74-9821-4ad17596aef2","revisionId":"13c1861b-de83-4f9f-aff1-806196d8026b","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"cc790568-cf0f-4bf7-8ef4-3aaab4534775","label":"","content":"Solve $\\frac{5}{x + 3} + \\frac{2}{x - 3} = 1$","markscheme":"- Multiply by common denominator: $5(x - 3) + 2(x + 3) = (x + 3)(x - 3)$ M1\n- Expand and simplify: $7x - 9 = x^2 - 9$ M1\n- Rearrange to $x^2 - 7x = 0$ M1\n- Factorise $x(x - 7) = 0$ to get $x = 0$ or $x = 7$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Multiply by common denominator $(x + 3)(x - 3)$. ","code":"M"},{"id":"p2","marks":1,"description":"Expand terms and simplify to a linear expression on one side and $x^2 - 9$ on the other.","code":"M"},{"id":"p3","marks":1,"description":"Rearrange to form a quadratic equation $x^2 - 7x = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Factorise and solve to find $x = 0$ and $x = 7$.","code":"A"}],"finalAnswers":["x = 0, x = 7"],"generatedAt":"2026-08-10T10:36:32.361Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"bc423aba-0e6a-4213-b0e8-b1435123f4c2","revisionId":"d1616658-4908-4bf1-9653-62e72e71e5d3","questionNumber":null,"questionType":"LA","specification":"Given that\n\n$$x + 1 : x + 4 = x - 2 : 2x - 8$$","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"6940cedd-17f6-4944-93fa-f8a31592438c","label":"a","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{x+1}{x+4} = \\frac{x-2}{2x-8}$ M1\n- Cross multiply: $(x+1)(2x-8) = (x+4)(x-2)$ M1\n- Expand and simplify to $x^2 - 8x = 0$ M1\n- Solve to get $x = 0$ and $x = 8$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Sets up the equation using fractions $\\frac{x+1}{x+4} = \\frac{x-2}{2x-8}$","code":"M"},{"id":"p2","marks":1,"description":"Cross multiplies to remove fractions $(x+1)(2x-8) = (x+4)(x-2)$","code":"M"},{"id":"p3","marks":1,"description":"Expands brackets and simplifies to the quadratic equation $x^2 - 8x = 0$","code":"M"},{"id":"p4","marks":1,"description":"Solves the quadratic equation to find both $x = 0$ and $x = 8$","code":"A"}],"finalAnswers":["0, 8","x = 0, x = 8","8, 0"],"generatedAt":"2026-08-10T10:37:29.298Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"c233ea6e-feda-4890-bcd6-ab2bd6933d5d","revisionId":"b735cae6-c53f-402d-adc0-9f82bb047fbc","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"hard","totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"849bb0ba-0946-417b-b87c-97f0d671ef76","label":"a","content":"Simplify fully $\\frac{4x^2 + 28x}{x^2 - 49}$","markscheme":"- Factorise numerator and denominator: $\\frac{4x(x+7)}{(x-7)(x+7)}$ M1\n- Simplify by cancelling $(x+7)$ to get $\\frac{4x}{x-7}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Factorise numerator as $4x(x+7)$ and denominator as $(x-7)(x+7)$.","code":"M"},{"id":"p2","marks":1,"description":"Simplify by cancelling the common factor $(x+7)$ to reach the final answer.","code":"A"}],"finalAnswers":["\\frac{4x}{x-7}"],"generatedAt":"2026-08-10T10:39:01.008Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null}],"subjectCode":"gcs

Algebraic Fractions

Question 29

Algebraic Fractions Questions

Algebraic Fractions

Question 29

Algebraic Fractions Questions