#### Answer

$\text{all real numbers except }$ $
t=-\dfrac{5}{4}
$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
The domain of the given rational function, $
p(t)=\dfrac{3t-7}{4t+5}
,$ are the values of $
t
$ which will NOT make the denominator equal to $0.$
$\bf{\text{Solution Details:}}$
Solving for the values of $
t
$ that will make the denominator equal to $0$ results to
\begin{array}{l}\require{cancel}
4t+5=0
\\\\
4t=-5
\\\\
t=-\dfrac{5}{4}
.\end{array}
Hence, the domain is the set of $
\text{all real numbers except }$ $
t=-\dfrac{5}{4}
.$