Answer
Domain is all real numbers except $0$.
Work Step by Step
Given $f(x)=\frac{x-2}{x^3+x}$.
Determine the values of $x$ that will make the function undefined.
The function is undefiend when the denominator is equal to zero, thus:
${x^3+x}\ne0$
$x(x^2+1)\ne0$
Use the Zero-Product Property, we obtain:
\begin{align*}
x&\ne0 &\text{ or }& &x^2+1\ne0\\
x&\ne0 &\text{ or }& &x^2\ne-1\\
\end{align*}
No real number $x$ will have $x^2=-1$.
Thus, the only number that makes the function undefined is $0$.
Therefore, the domain is
{$x|x\ne0$}
