#### Answer

$
\text{all real numbers except }$ $
a=-\dfrac{7}{2},3
.$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
The domain of the given rational function, $
h(a)=\dfrac{3a-1}{(2a+7)(a-3)}
,$ are the values of $
a
$ which will NOT make the denominator equal to $0.$
$\bf{\text{Solution Details:}}$
Solving for the values of $
a
$ that will make the denominator equal to $0$ results to
\begin{array}{l}\require{cancel}
(2a+7)(a-3)=0
.\end{array}
Equating each factor to zero (Zero Product Property), then
\begin{array}{l}\require{cancel}
2a+7=0
\\\\\text{OR}\\\\
a-3=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2a=-7
\\\\
a=-\dfrac{7}{2}
\\\\\text{OR}\\\\
a-3=0
\\\\
a=3
.\end{array}
Hence, the domain is the set of $
\text{all real numbers except }$ $
a=-\dfrac{7}{2},3
.$