Simplify (x^2-4)/(x^2+2x)

$\frac{x^{2} - 4}{x^{2} + 2 x}$

Step 1

Simplify the numerator.

Rewrite $4$ as $2^{2}$ .

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

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 $b = 2$ .

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

Step 2

Simplify terms.

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

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

$\frac{(x + 2) (x - 2)}{x \cdot x + 2 x}$

Factor $x$ out of $2 x$ .

$\frac{(x + 2) (x - 2)}{x \cdot x + x \cdot 2}$

Factor $x$ out of $x \cdot x + x \cdot 2$ .

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

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x - 2}{x}$