# How do you find the domain of f(x)=(-3x^2)/(x^2+4x-45)?

Aug 5, 2016

Domain: all Real values except $\left(- 9\right)$ and $\left(+ 5\right)$

#### Explanation:

$f \left(x\right) = \frac{- 3 {x}^{2}}{{x}^{2} + 4 x - 45}$
$\textcolor{w h i t e}{\text{XXX}}$will be defined for all Real values of $x$
$\textcolor{w h i t e}{\text{XXX}}$except those values which cause the denominator to be equal to zero.

That is the Domain will be all $\mathbb{R}$
except when
$\textcolor{w h i t e}{\text{XXX}} {x}^{2} + 4 x - 45 = 0$

Factoring:
$\textcolor{w h i t e}{\text{XXX}} \left(x + 9\right) \left(x - 5\right) = 0$

So the Domain of $f \left(x\right)$ is
$\textcolor{w h i t e}{\text{XXX}} \mathbb{R} - \left\{- 9 , + 5\right\}$