Simplify (x^2-1)/(5x^2+5x)

$\frac{x^{2} - 1}{5 x^{2} + 5 x}$

Step 1

Simplify the numerator.

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

$\frac{x^{2} - 1^{2}}{5 x^{2} + 5 x}$

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 $b = 1$ .

$\frac{(x + 1) (x - 1)}{5 x^{2} + 5 x}$

Step 2

Simplify terms.

Factor $5 x$ out of $5 x^{2} + 5 x$ .

Factor $5 x$ out of $5 x^{2}$ .

$\frac{(x + 1) (x - 1)}{5 x (x) + 5 x}$

Factor $5 x$ out of $5 x$ .

$\frac{(x + 1) (x - 1)}{5 x (x) + 5 x (1)}$

Factor $5 x$ out of $5 x (x) + 5 x (1)$ .

$\frac{(x + 1) (x - 1)}{5 x (x + 1)}$

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{(x + 1) (x - 1)}{5 x (x + 1)}$

Rewrite the expression.

$\frac{x - 1}{5 x}$