# How do you simplify (x^2 - x - 6) /( x^2 - 4)?

Jun 24, 2016

$= \frac{x - 3}{x - 2}$

#### Explanation:

We may not cancel in the numerator or denominator because there is not only one term. The + and - signs show there are 3 terms in the numerator an two terms in the denominator.

However, if we factorise we will only have one term and then we may cancel.
The numerator is a quadratic trinomial and the denominator is the difference between two squares.

$\frac{{x}^{2} - x - 6}{{x}^{2} - 4} = \frac{\left(x - 3\right) \left(x + 2\right)}{\left(x + 2\right) \left(x - 2\right)}$

$\frac{\left(x - 3\right) \cancel{\left(x + 2\right)}}{\cancel{\left(x + 2\right)} \left(x - 2\right)}$

$= \frac{x - 3}{x - 2}$