# How do you simplify (x^2 – x – 6 )/(x^2 – 9x + 18 )?

Apr 23, 2016

$\frac{{x}^{2} - x - 6}{{x}^{2} - 9 x + 18} = \frac{x + 2}{x - 6} = 1 + \frac{8}{x - 6}$

excluding $x = 3$

#### Explanation:

Factor the numerator and denominator. Cancel the common factor $\left(x - 3\right)$, noting that $x = 3$ is an excluded value. Simplify...

$\frac{{x}^{2} - x - 6}{{x}^{2} - 9 x + 18}$

$= \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - 3\right)}}} \left(x + 2\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - 3\right)}}} \left(x - 6\right)}$

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

$= \frac{x - 6 + 8}{x - 6}$

$= 1 + \frac{8}{x - 6}$

excluding $x = 3$.

The value $x = 3$ must be excluded since the numerator and denominator of the original rational expression are both zero, resulting in an undefined value, whereas the simplified expression is well defined when $x = 3$.