Answer
$\text{all real numbers except }$ $
n=\left\{ -10,-4 \right\}
$
Work Step by Step
$\bf{\text{Solution Outline:}}$
The domain of the given rational function, $
C(n)=\dfrac{n+10}{(n+4)(n+10)}
,$ are the values of $
n
$ which will NOT make the denominator equal to $0.$
$\bf{\text{Solution Details:}}$
Solving for the values of $
n
$ that will make the denominator equal to $0$ results to
\begin{array}{l}\require{cancel}
(n+4)(n+10)=0
.\end{array}
Equating each factor to zero (Zero Product Property), then
\begin{array}{l}\require{cancel}
n+4=0
\\\\\text{OR}\\\\
n+10=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
n+4=0
\\\\
n=-4
\\\\\text{OR}\\\\
n+10=0
\\\\
n=-10
.\end{array}
Hence, the domain is the set of $
\text{all real numbers except }$ $
n=\left\{ -10,-4 \right\}
.$
