Simplify (x+1)/(x^3-x)

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

Step 1

Simplify the denominator.

Factor $x$ out of $x^{3} - x$ .

Factor $x$ out of $x^{3}$ .

$\frac{x + 1}{x \cdot x^{2} - x}$

Factor $x$ out of $- x$ .

$\frac{x + 1}{x \cdot x^{2} + x \cdot - 1}$

Factor $x$ out of $x \cdot x^{2} + x \cdot - 1$ .

$\frac{x + 1}{x (x^{2} - 1)}$

Rewrite $1$ as $1^{2}$ .

$\frac{x + 1}{x (x^{2} - 1^{2})}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$\frac{x + 1}{x (x + 1) (x - 1)}$

Step 2

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{x + 1}{x (x + 1) (x - 1)}$

Rewrite the expression.

$\frac{1}{x (x - 1)}$