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