Find the Holes in the Graph f(x)=(-4x^2-16x)/(3x^2)

$f (x) = \frac{- 4 x^{2} - 16 x}{3 x^{2}}$

Step 1

Factor $4 x$ out of $- 4 x^{2} - 16 x$ .

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

$f (x) = \frac{4 x (- x) - 16 x}{3 x^{2}}$

Factor $4 x$ out of $- 16 x$ .

$f (x) = \frac{4 x (- x) + 4 x (- 4)}{3 x^{2}}$

Factor $4 x$ out of $4 x (- x) + 4 x (- 4)$ .

$f (x) = \frac{4 x (- x - 4)}{3 x^{2}}$

Step 2

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

Factor $x$ out of $4 x (- x - 4)$ .

$f (x) = \frac{x (4 (- x - 4))}{3 x^{2}}$

Cancel the common factors.

Factor $x$ out of $3 x^{2}$ .

$f (x) = \frac{x (4 (- x - 4))}{x (3 x)}$

Cancel the common factor.

$f (x) = \frac{x (4 (- x - 4))}{x (3 x)}$

Rewrite the expression.

$f (x) = \frac{4 (- x - 4)}{3 x}$

Step 3

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

No holes

Step 4