Find the Holes in the Graph f(x)=(x^2-64)/(x-6)

$f (x) = \frac{x^{2} - 64}{x - 6}$

Step 1

Factor $x^{2} - 64$ .

Rewrite $64$ as $8^{2}$ .

$f (x) = \frac{x^{2} - 8^{2}}{x - 6}$

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 $b = 8$ .

$f (x) = \frac{(x + 8) (x - 8)}{x - 6}$

Step 2

Since no factors can be removed from the denominator, there are no holes in the graph.

No holes

Step 3