A-level · Algebra & functions

Algebraic fractionsExam-style questions

Fractions with letters in them, handled by the rules of number fractions. What may cancel and why; factorising before cancelling; adding and subtracting over a common denominator, with the minus sign kept on the whole top; multiplying, and dividing by the reciprocal; solving equations with fractions and rejecting answers that make a denominator zero; and writing a top-heavy fraction as a quotient plus a remainder.

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20 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
Simplify $\dfrac{x^{2} + 5x + 6}{x^{2} - 4}$ . (2 marks)
Level 2 · 2 marksTry it
2
(a) Simplify fully

$\dfrac{2x^2 - x - 6}{x^2 - 4}$ . (3 marks)
(b) Hence solve the equation $\dfrac{2x^2 - x - 6}{x^2 - 4} = 3$ . (2 marks)
Level 2 · 5 marksTry it
3
The function f is defined by

$\text{f}(x) = \dfrac{2x^2 + 7x + 3}{x^2 - x - 12} - \dfrac{6}{x - 4} \qquad x > 4$
(a) Show that

$\text{f}(x) = \dfrac{2x - 5}{x - 4} \qquad x > 4$

(3 marks)
(b) Hence find $\text{f}'(x)$ giving your answer in simplest form.

(2 marks)
Level 2 · 5 marksTry it
4
Simplify $\dfrac{x^2 - 4}{x + 1} \div \dfrac{x + 2}{x^2 - 1}$ .
Level 3 · 3 marksTry it
5
(a) Given that $\dfrac{x^{2} + 3x + 5}{x + 2} \equiv x + 1 + \dfrac{R}{x + 2}$ , find the value of $R$ . (3 marks)
(b) Hence solve $\dfrac{x^{2} + 3x + 5}{x + 2} = x + 2$ . (2 marks)
Level 3 · 5 marksTry it

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