#### Answer

$\text{all real numbers except }$ $
x=\left\{ -4,9 \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
The domain of the given rational function, $
g(x)=\dfrac{2x-7}{(x+4)(x-9)}
,$ are the values of $
x
$ which will NOT make the denominator equal to $0.$
$\bf{\text{Solution Details:}}$
Solving for the values of $
x
$ that will make the denominator equal to $0$ results to
\begin{array}{l}\require{cancel}
(x+4)(x-9)
.\end{array}
Equating each factor to zero (Zero Product Property), then
\begin{array}{l}\require{cancel}
x+4=0
\\\\\text{OR}\\\\
x-9=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x+4=0
\\\\
x=-4
\\\\\text{OR}\\\\
x-9=0
\\\\
x=9
.\end{array}
Hence, the domain is the set of $
\text{all real numbers except }$ $
x=\left\{ -4,9 \right\}
.$