Edexcel IGCSE Math A 2.2.HC Manipulating Algebraic Fractions

Practise combining and simplifying algebraic fractions whose numerators or denominators may be numerical, linear or quadratic.

Exam points

form a common denominator before combining algebraic fractions into one fraction
factorise linear or quadratic expressions before cancelling valid common factors
show clear algebraic working when proving a fraction simplifies to a stated form

[Maximum number: 3]

Express $\frac{4}{x-2}-\frac{3}{x+1}$ as a single fraction.
Give your answer in its simplest form.

$\frac{4}{x-2}-\frac{3}{x+1} =\frac{4(x+1)-3(x-2)}{(x-2)(x+1)}$ $=\frac{4x+4-3x+6}{(x-2)(x+1)} =\frac{x+10}{(x-2)(x+1)}$

Equivalent denominator accepted:
$\frac{x+10}{x^2-x-2}$

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2.2.HC Algebraic fractions question 1