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

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
Simplify fully $\dfrac{x^2 - 4}{x^2 + 5x + 6}$ (3 marks)
Level 4 · 3 marksTry it
2
Simplify fully $\dfrac{2x^2 + 5x - 3}{x^2 - 9}$ (3 marks)
Level 4 · 3 marksTry it
3
Show that

$\frac{2x^2 + 7x - 15}{4x^2 - 9}$

can be written in the form $\dfrac{ax + b}{cx + d}$ where $a$ , $b$ , $c$ and $d$ are integers.

(3 marks)
Level 4 · 3 marksTry it
4
Simplify fully $\dfrac{x^2 + 5x}{x^2 - 25}$
Level 4 · 3 marksTry it
5
Simplify fully $\dfrac{x^2 + 7x + 12}{x^2 - 9}$
Level 4 · 3 marksTry it

2 more questions on simplifying, multiplying and dividing algebraic fractions

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