GCSE · Algebraic fractions

Equations with algebraic fractionsExam-style questions

Why multiplying through by the denominators turns a fraction equation into a polynomial one, when the result is linear versus quadratic, and the grade-9 pattern where 1/x-terms breed a quadratic.

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12 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    Solve 12x−1=3\dfrac{12}{x - 1} = 3
    Level 2 · 2 marksTry it
  2. 2
    Solve 3x+4=5\dfrac{3}{x} + 4 = 5
    Level 3 · 2 marksTry it
  3. 3
    Solve x+23=2x−54\dfrac{x + 2}{3} = \dfrac{2x - 5}{4}
    Level 3 · 3 marksTry it
  4. 4
    Solve 3x+1+2x−2=1\dfrac{3}{x + 1} + \dfrac{2}{x - 2} = 1

    Give your solutions correct to 2 decimal places. (4 marks)
    Level 4 · 4 marksTry it
  5. 5
    Solve 3x+2+42x−3=1\dfrac{3}{x + 2} + \dfrac{4}{2x - 3} = 1

    (4 marks)
    Level 4 · 4 marksTry it

7 more questions on equations with algebraic fractions

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