Answer
Domain = $\mathbb{R}\backslash\{-3,3\}$ or $\{x\in \mathbb{R}\ |\ x\neq\pm 3\}$
Work Step by Step
The domain of a real function ( a function defined on real numbers)
is the set of numbers for which f(x) is defined.
$ f(x)=\displaystyle \frac{5}{x^{2}-9}\quad$ can be calculated for any real number,
except for those yielding a zero in the denominator.
Here,
$x^{2}-=0$
$x^{2}=9$
$x=\pm 3 \quad $must be excluded from the domain.
Domain = $\mathbb{R}\backslash\{-3,3\}$ or $\{x\in \mathbb{R}\ |\ x\neq\pm 3\}$
