# How do you simplify (x^2 - 7x + 6)/(x^2-36)?

Jul 27, 2016

(x^2-7x+6)/(x^2-36)=color(green)((x-1)/(x+6)
(assuming $x \ne \pm 6$ so the original expression is valid).

#### Explanation:

Factoring
$\textcolor{w h i t e}{\text{XXX}} {x}^{2} - 7 x + 6 = \left(x - 6\right) \left(x - 1\right)$

$\textcolor{w h i t e}{\text{XXX}} {x}^{2} - 36 = \left(x - 6\right) \left(x + 6\right)$

So
$\textcolor{w h i t e}{\text{XXX")(x^2-7x+6)/(x^2-36)=(cancel(""(x-6))(x-1))/(cancel(} \left(x - 6\right)} \left(x + 6\right)$