domain of 1/(x^3-x) — step-by-step solution

Let's evaluate the domain of

\frac{1}{x^{3} - x}

For the expression

\frac{1}{x^{3} - x}

to exist, you must check:

x^{3} - x \neq 0

You can factorize the expression:

x^{3} - x

into:

x \cdot (x^{2} - 1)

Solution found:

x \neq 0

Let's solve in

ℝ

x^{2} - 1 \neq 0

Solution found:

x \in ℝ \ {-1, 1}

▶Domain of definition:

x \in ℝ \ {-1, 0, 1}