# What is the domain of h(x)= x / (x ^2 - x - 6)?

Sep 7, 2015

$x \in \mathbb{R} - \left\{- 2. 3\right\}$

#### Explanation:

$h \left(x\right) = \frac{x}{{x}^{2} - x - 6}$ is defined for all Real values of $x$
except those values for which ${x}^{2} - x - 6 = 0$

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

So if $x = - 2$ or $x = 3$
$\textcolor{w h i t e}{\text{XXXX}} {x}^{2} - x - 6 = 0$
and
$\textcolor{w h i t e}{\text{XXXX}} h \left(x\right)$ is undefined