Pre-Algebra Examples

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

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

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

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

Step 1.2

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 $b = 3$ .

$\frac{x - 4}{(x + 3) (x - 3)}$

Step 2

Split the fraction $\frac{x - 4}{(x + 3) (x - 3)}$ into two fractions.

$\frac{x}{(x + 3) (x - 3)} + \frac{- 4}{(x + 3) (x - 3)}$

Step 3

Move the negative in front of the fraction.

$\frac{x}{(x + 3) (x - 3)} - \frac{4}{(x + 3) (x - 3)}$