# What is the domain of f(x) = (x^2 - x - 6) /( x^2 + x - 12)?

Oct 7, 2015

Domain: $\mathbb{R} - \left\{- 4 , + 3\right\}$

#### Explanation:

$f \left(x\right) = \frac{{x}^{2} - x - 6}{{x}^{2} + x - 12}$
is defined for all Real values of $x$ except those that cause ${x}^{2} + x - 12 = 0$

Since $\left({x}^{2} + x - 1\right) = \left(x + 4\right) \left(x - 3\right)$

$\textcolor{w h i t e}{\text{XXX}} x = - 4$ and $x = 3$
cause ${x}^{2} + x - 12 = 0$
and are therefore forbidden from the Domain of $f \left(x\right)$