Simplify (x^2-4)/(x^2-9)

$\frac{x^{2} - 4}{x^{2} - 9}$

Step 1

Simplify the numerator.

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

$\frac{x^{2} - 2^{2}}{x^{2} - 9}$

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 $b = 2$ .

$\frac{(x + 2) (x - 2)}{x^{2} - 9}$

Step 2

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

$\frac{(x + 2) (x - 2)}{x^{2} - 3^{2}}$

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 $b = 3$ .

$\frac{(x + 2) (x - 2)}{(x + 3) (x - 3)}$