Find the Holes in the Graph y=(x^2-25)/(x-4)

$y = \frac{x^{2} - 25}{x - 4}$

Step 1

Factor $x^{2} - 25$ .

Rewrite $25$ as $5^{2}$ .

$y = \frac{x^{2} - 5^{2}}{x - 4}$

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 $b = 5$ .

$y = \frac{(x + 5) (x - 5)}{x - 4}$

Step 2

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

No holes

Step 3