Precalculus Examples

$f (x) = \frac{1}{(x^{2} - 4) (x - 4)}$

Step 1

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

$f (x) = \frac{1}{(x^{2} - 2^{2}) (x - 4)}$

Step 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 $b = 2$ .

$f (x) = \frac{1}{(x + 2) (x - 2) (x - 4)}$