# How do you find the domain in interval notation for f(x)=(x+4)/(x^2-4) ?

May 30, 2015

$f \left(x\right) = \frac{x + 4}{{x}^{2} - 4}$

$f \left(x\right) = \frac{x + 4}{\textcolor{red}{{\left(x\right)}^{2} - {\left(2\right)}^{2}}}$

$f \left(x\right) = \frac{x + 4}{\textcolor{red}{\left(x + 2\right) \left(x - 2\right)}}$ $\Leftarrow {\left(a\right)}^{2} - {\left(b\right)}^{2} = \left(a + b\right) \left(a - b\right)$

$x$ can not be $- 2$ or $2$, otherwise $f \left(x\right) = \infty$

Domain:
$x \in \mathbb{R}$ except $- 2$ and $2$.