Find the Holes in the Graph f(x)=(5x^2-25x)/(-4x^2)

$f (x) = \frac{5 x^{2} - 25 x}{- 4 x^{2}}$

Step 1

Factor $5 x$ out of $5 x^{2} - 25 x$ .

Factor $5 x$ out of $5 x^{2}$ .

$f (x) = \frac{5 x (x) - 25 x}{- 4 x^{2}}$

Factor $5 x$ out of $- 25 x$ .

$f (x) = \frac{5 x (x) + 5 x (- 5)}{- 4 x^{2}}$

Factor $5 x$ out of $5 x (x) + 5 x (- 5)$ .

$f (x) = \frac{5 x (x - 5)}{- 4 x^{2}}$

Step 2

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $5 x (x - 5)$ .

$f (x) = \frac{x (5 (x - 5))}{- 4 x^{2}}$

Cancel the common factors.

Factor $x$ out of $- 4 x^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Move the negative in front of the fraction.

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

Step 4

Multiply $4$ by $x$ .

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

Step 5

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

No holes

Step 6