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Simplifying fractions

A fraction with letters cancels only when the numerator and the denominator share a factor. Terms that are added cannot be struck against each other. Factorise first, cancel common factors, and finally write down the values that make the denominator zero. The fraction is not defined there, even if the simplified expression gives a number. The difference of squares is the most common factorisation in this course.

\frac{x^2 - a^2}{x - a} = x + a

for x not equal to a

x^2 - a^2 = (x - a)(x + a)

difference of squares

Symbols

$x$	the variable
$a$	a number

Example

$\dfrac{x^2 - 9}{x + 3} = x - 3$ for $x \ne -3$ . Check with $x = 5$ : $\dfrac{25 - 9}{5 + 3} = 2$ and $5 - 3 = 2$ .

Cancel factors, not terms. Always check that the denominator does not become zero.

Practise algebra and equations for free →

Equations with fractions →

Part of Mathematics S1: Algebra and equations.