Precalculus Examples

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

Step 1

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

$\frac{x}{{(3 x)}^{2} - 4}$

Step 2

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

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

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 x$ and $b = 2$ .

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