# How do you simplify (x-2)/(x^2-8x+12 )?

Sep 29, 2015

$\frac{1}{x - 6}$

#### Explanation:

First, factor the denominator completely.

$\frac{x - 2}{{x}^{2} - 8 x + 12}$
$= \frac{x - 2}{\left(x - 2\right) \left(x - 6\right)}$
$= \frac{\cancel{x - 2}}{\cancel{\left(x - 2\right)} \left(x - 6\right)}$
$\textcolor{b l u e}{= \frac{1}{x - 6}}$

WARNING: You can simplify this, however, take note that you have canceled out $\left(x - 2\right)$ in the denominator. If you are asked for the domain, make sure that $\textcolor{red}{x - 2 \ne 0}$ or $\textcolor{red}{x \ne 2}$.