Answer
The domain is all real numbers except $0$ and $-8$.
Work Step by Step
To find the values of $x$ at which the denominator equals zero, set the denominator equal to zero and solve.
$x^{2}+8x=0$
Factor:
$x(x+8)=0$
Using the Zero Product Property
$x=0$ and $x+8=0$
The first equation is already solved:
$x=0$
The second equation:
$x+8=0$
Subtract $8$ from both sides
$x=-8$
These two values of $x$, $0$ and $-8$, create an undefined fraction within the function. Therefore, the domain is all real numbers EXCEPT $0$ and $-8$.
