#### Answer

$\left( -\infty, 7 \right)\cup(7,\infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
The domain of the given function, $
f(x)=\dfrac{x}{x-7}
,$ is all the values of $x$ for which the denominator is not equal to $0.$ Express the answer in the interval notation.
$\bf{\text{Solution Details:}}$
Since the denominator cannot be zero, then
\begin{array}{l}\require{cancel}
x-7\ne0
\\\\
x\ne7
.\end{array}
Hence, the domain is $
\left( -\infty, 7 \right)\cup(7,\infty)
.$