Simplify (x^2-1)/(x^2+x)

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

Simplify the numerator.

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

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

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 $b = 1$ .

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

Simplify terms.

Factor $x$ out of $x^{2} + x$ .

Factor $x$ out of $x^{2}$ .

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

Raise $x$ to the power of $1$ .

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

Factor $x$ out of $x^{1}$ .

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

Factor $x$ out of $x \cdot x + x \cdot 1$ .

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

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

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