#### Answer

The domain of $R(x)$ is the set of all real numbers except $3$ and $-3$.
In set notation: $\text{Domain:} \{x|x \neq 3, \hspace{5pt} x \neq -3\}$

#### Work Step by Step

Rational functions are of the form
$$R(x)=\dfrac{p(x)}{q(x)}$$
The domain of the rational function is the set of all real numbers except those for which the denominator $q(x)$ is $0$.
$\text{Set the denominator equal to zero then solve:}$
$$4(x^2-9)=0\\[3mm] \text{By Factoring:} \\
4(x-3)(x+3)=0\\
\text{Using the zero product property:}\\
x-3=0 \hspace{10pt} \text{ or }\hspace{10pt} x+3=0\\
x=3 \hspace{10pt} \text{ or }\hspace{10pt} x=-3$$
Thus, the domain of $R(x)$ is the set of all real numbers except $3$ and $-3$.
$\text{Domain:} \{x|x \neq 3, \hspace{5pt} x \neq -3\}$