Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$(-\infty, -3)\cup(-3,\infty)$
$\bf{\text{Solution Outline:}}$ 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 $(-\infty, -3)\cup(-3,\infty) .$