# How do you simplify (x^2-3x+2)/(x^2+5x-6)?

Sep 7, 2016

$\frac{x - 2}{x + 6}$

#### Explanation:

The first step is to factorise both numerator and denominator.

Both are quadratics and can be factorised using the a-c method.

$\Rightarrow {x}^{2} - 3 x + 2 = \left(x - 2\right) \left(x - 1\right)$

and ${x}^{2} + 5 x - 6 = \left(x + 6\right) \left(x - 1\right)$

$\Rightarrow \frac{{x}^{2} - 3 x + 2}{{x}^{2} + 5 x - 6} = \frac{\left(x - 2\right) \left(\cancel{x - 1}\right)}{\left(x + 6\right) \left(\cancel{x - 1}\right)} = \frac{x - 2}{x + 6}$