Answer
The domain of $G(x)$ is the set of all real numbers $x$ except $-3$ and $4$.
In set notation: $\text{Domain:} \{x|x \neq 4, \hspace{5pt} x \neq -3\}$
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 $0$.
$\text{Set the denominator equal to zero the solve:}$
$$(x+3)(4-x)= 0\\[3mm] \text{Using the zero-product property:} \\[3mm] x+3=0 \text{ or } x-4=0
\\x =-3 \hspace{10pt} \text{or} \hspace{10pt} x=4$$
Thus, the domain of $G(x)$ is the set of all real numbers $x$ except $-3$ and $4$.
$\text{Domain:} \{x|x \neq 4, \hspace{5pt} x \neq -3\}$
