#### Answer

$\text{all real numbers except }$ $
t=\left\{ -7,7 \right\}
$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
The domain of the given rational function, $
h(t)=\dfrac{t+7}{t^2-49}
,$ are the values of $
t
$ which will NOT make the denominator equal to $0.$
$\bf{\text{Solution Details:}}$
The values of $
t
$ that will make the denominator equal to $0$ are
\begin{array}{l}\require{cancel}
t^2-49=0
.\end{array}
Using the factoring of the difference of $2$ squares, which is given by $a^2-b^2=(a+b)(a-b),$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
(t+7)(t-7)=0
.\end{array}
Equating each factor to zero (Zero Product Property), then
\begin{array}{l}\require{cancel}
t+7=0
\\\\\text{OR}\\\\
t-7=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
t+7=0
\\\\
t=-7
\\\\\text{OR}\\\\
t-7=0
\\\\
t=7
.\end{array}
Hence, the domain is the set of $
\text{all real numbers except }$ $
t=\left\{ -7,7 \right\}
.$