/grade-7-7-6-algebraic-fractions/questions","formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-maths/gcse-formulae-to-remember.pdf","initialIndex":43,"initialQuestionWindow":[{"id":"7e629eee-78fa-4580-b518-91172efb8f4d","revisionId":"f270cbb9-0e39-4c9d-b326-ef6a388de618","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"hard","totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"5e1a19d2-4bdb-4963-94d7-a9f34f032549","label":"a","content":"Simplify fully $\\frac{x^2 + 2x - 8}{x^2 + 6x + 8}$","markscheme":"- Factorise numerator and denominator: $\\frac{(x+4)(x-2)}{(x+4)(x+2)}$ M1\n- Simplify by cancelling $(x+4)$ to get $\\frac{x-2}{x+2}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Attempt to factorise both numerator and denominator into two brackets, with at least one quadratic factorised correctly.","code":"M"},{"id":"p2","marks":1,"description":"Correct simplified fraction after cancelling common factors.","code":"A"}],"finalAnswers":["\\frac{x-2}{x+2}"],"generatedAt":"2026-08-10T10:36:49.070Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"97b840f5-2197-4f0a-b907-620431f32819","revisionId":"9eb98cf3-d13f-45a7-9347-1e8b83e74e3a","questionNumber":null,"questionType":"LA","specification":"Given that\n\n$$2x - 1 : x + 2 = 3x - 3 : x + 3$$","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"cec861b8-4913-4cdf-bcf5-14761a7a6331","label":"a","content":"Find the possible values of $x$.","markscheme":"- Set up equation: $\\frac{2x-1}{x+2} = \\frac{3x-3}{x+3}$ M1\n- Cross multiply: $(2x-1)(x+3) = (x+2)(3x-3)$ M1\n- Expand and simplify to $x^2 - 2x - 3 = 0$ M1\n- Solve to get $x = 3$ and $x = -1$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Sets up the equation using fractions $\\frac{2x-1}{x+2} = \\frac{3x-3}{x+3}$","code":"M"},{"id":"p2","marks":1,"description":"Cross multiplies to remove fractions $(2x-1)(x+3) = (x+2)(3x-3)$","code":"M"},{"id":"p3","marks":1,"description":"Expands brackets and simplifies to the quadratic equation $x^2 - 2x - 3 = 0$","code":"M"},{"id":"p4","marks":1,"description":"Solves the quadratic equation to find both $x = 3$ and $x = -1$","code":"A"}],"finalAnswers":["3, -1","x = 3, x = -1","-1, 3"],"generatedAt":"2026-08-10T10:37:32.322Z","modelVersion":"gemini-3-flash-preview"},"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"ab4659be-4d0d-44e0-b43f-1b830c59ad29","revisionId":"1af0de4b-d93f-410c-9402-575ac22c3bd0","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"hard","totalMarks":4,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"55d25f81-c91f-4268-be35-e2a36bd0f979","label":"a","content":"Solve $\\frac{5}{y - 3} - \\frac{2}{y + 1} = 1$","markscheme":"- Multiply by common denominator: $5(y + 1) - 2(y - 3) = 1(y - 3)(y + 1)$ M1\n- Expand and simplify: $3y + 11 = y^2 - 2y - 3$ M1\n- Rearrange to $y^2 - 5y - 14 = 0$ M1\n- Factorise $(y - 7)(y + 2) = 0$ to get $y = 7$ or $y = -2$ A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Multiply the equation by the common denominator $(y-3)(y+1)$.","code":"M"},{"id":"p2","marks":1,"description":"Expand the brackets and simplify the expressions on both sides.","code":"M"},{"id":"p3","marks":1,"description":"Rearrange the expression into the quadratic form $y^2 - 5y - 14 = 0$.","code":"M"},{"id":"p4","marks":1,"description":"Factorise and solve the quadratic equation to find both $y$ values.","code":"A"}],"finalAnswers":["y = 7, y = -2"],"generatedAt":"2026-08-10T10:36:37.963Z","modelVersion":"gemini-3-flash-preview"},"exp

Algebraic Fractions

Question 42

Algebraic Fractions Questions

Algebraic Fractions

Question 42

Algebraic Fractions Questions