#### Answer

$(-\infty,4) \cup (4,\infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
The domain of the given function, $
f(x)=\dfrac{x+3}{2x-8}
,$ is all values of $x$ for which the denominator is not $0.$ Express the answer in interval notation.
$\bf{\text{Solution Details:}}$
Since the denominator of the given function cannot be $0$, then
\begin{array}{l}\require{cancel}
2x-8\ne0
\\\\
2x\ne8
\\\\
x\ne\dfrac{8}{2}
\\\\
x\ne4
.\end{array}
Hence the domain is $
(-\infty,4) \cup (4,\infty)
.$