# How do you find the domain in interval notation for f(x)=x/(x^3+8) ?

$\left({x}^{3} + 8\right) = \left({x}^{3} + {2}^{3}\right) = \left(x + 2\right) \left({x}^{2} - 2 x + 4\right)$
has only one zero for real values of $x$, viz $x = - 2$.
$f \left(x\right)$ is well defined for all other values of $x$.
So the domain of $f \left(x\right)$ is $\left(- \infty , - 2\right) \cup \left(- 2 , \infty\right)$