## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$(c)$
The domain of a rational expression is the whole set of real numbers, excluding the numbers that yield zero in the denominator. Here, we exclude $x$ for which denominator = 0 $x^{3}+x=0\qquad$... factor out x... $x(x^{2}+1)=0$ By the zero product principle, at least one of the factors is zero. $x^{2}+1$ is never zero, because $x^{2}\geq 0$. So, the only number to exclude from the domain is $x=0$.