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 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
  2. 2
    Solve 3x+2+42x−3=1\dfrac{3}{x + 2} + \dfrac{4}{2x - 3} = 1

    (4 marks)
    Level 4 · 4 marksTry it
  3. 3
    Solve 5x+32x=136\dfrac{5}{x} + \dfrac{3}{2x} = \dfrac{13}{6}
    Level 4 · 3 marksTry it
  4. 4
    Solve 3x+1=52x−1\dfrac{3}{x + 1} = \dfrac{5}{2x - 1}
    Level 4 · 3 marksTry it
  5. 5
    Solve 7x−23x=1912\dfrac{7}{x} - \dfrac{2}{3x} = \dfrac{19}{12}
    Level 4 · 3 marksTry it

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