Answer
$\color{blue}{(-\infty, -4) \cup (-4, +\infty)}$
Work Step by Step
Find the domain of each function:
For $f(x)$, the value of $x$ can be any real number.
Thus, domain of $f(x)$ is $(-\infty, +\infty)$.
For $g(x)$, the value of $x$ can be any real number.
Thus, the domain of $g(x)$ is $(-\infty, +\infty)$.
RECALL:
The domain of the $(f/g)(x)$ is the common elements of the domains of $f(x)$ and $g(x)$ excluding $x$ values for which $g(x)=0$.
Note that when $g(-4)=0$.
The intersection of the domains of $f$ and $g$ is $(-\infty, +\infty)$.
Thus, the domain of $(f/g)(x)$ is all real numbers except $-4$.
In interval notation, the domain of $f/g$ is:
$\color{blue}{(-\infty, -4) \cup (-4, +\infty)}$
