Find the Holes in the Graph f(x)=(x^2-10x)/(x^2-1)

$f (x) = \frac{x^{2} - 10 x}{x^{2} - 1}$

Step 1

Factor $x$ out of $x^{2} - 10 x$ .

Factor $x$ out of $x^{2}$ .

$f (x) = \frac{x \cdot x - 10 x}{x^{2} - 1}$

Factor $x$ out of $- 10 x$ .

$f (x) = \frac{x \cdot x + x \cdot - 10}{x^{2} - 1}$

Factor $x$ out of $x \cdot x + x \cdot - 10$ .

$f (x) = \frac{x (x - 10)}{x^{2} - 1}$

Step 2

Factor $x^{2} - 1$ .

Rewrite $1$ as $1^{2}$ .

$f (x) = \frac{x (x - 10)}{x^{2} - 1^{2}}$

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 $b = 1$ .

$f (x) = \frac{x (x - 10)}{(x + 1) (x - 1)}$

Step 3

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

No holes

Step 4