#### Answer

$(-\infty,-2) \cup (-2,\infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
The domain of the given function, $
f(x)=\dfrac{x-1}{3x+6}
,$ 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}
3x+6\ne0
\\\\
3x\ne-6
\\\\
x\ne-\dfrac{6}{3}
\\\\
x\ne-2
.\end{array}
Hence the domain is $
(-\infty,-2) \cup (-2,\infty)
.$