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

Jun 1, 2016

$\frac{{x}^{2} - x - 6}{{x}^{2} - 4} = \frac{x - 3}{x - 2}$

#### Explanation:

To simplify $\frac{{x}^{2} - x - 6}{{x}^{2} - 4}$, one needs to factorize numerator and denominator.

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

and ${x}^{2} - 4 = {x}^{2} - 2 x + 2 x - 4 = x \left(x - 2\right) + 2 \left(x - 2\right) = \left(x + 2\right) \left(x - 2\right)$

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

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