GCSE · Algebraic fractions

Simplifying, multiplying and dividing algebraic fractionsExam-style questions

Why only FACTORS cancel — never terms — so factorising must come first, and how × and ÷ work exactly as for number fractions once everything is in factors.

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

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    Simplify fully 2x2+x−3x2−1\dfrac{2x^2 + x - 3}{x^2 - 1}
    Level 5 · 3 marksTry it
  2. 2
    Simplify fully x2−45÷x+210\dfrac{x^2 - 4}{5} \div \dfrac{x + 2}{10}
    Level 5 · 3 marksTry it
  3. 3
    Simplify fully 2x2−7x−4x2−16\dfrac{2x^2 - 7x - 4}{x^2 - 16}
    Level 5 · 3 marksTry it
  4. 4
    Simplify fully x2+3xx2−1÷x+3x+1\dfrac{x^2 + 3x}{x^2 - 1} \div \dfrac{x + 3}{x + 1}
    Level 5 · 4 marksTry it