Find the Holes in the Graph f(x)=(-2x-8)/(4x-12)

$f (x) = \frac{- 2 x - 8}{4 x - 12}$

Factor $2$ out of $- 2 x - 8$ .

Factor $2$ out of $- 2 x$ .

$f (x) = \frac{2 (- x) - 8}{4 x - 12}$

Factor $2$ out of $- 8$ .

$f (x) = \frac{2 (- x) + 2 (- 4)}{4 x - 12}$

Factor $2$ out of $2 (- x) + 2 (- 4)$ .

$f (x) = \frac{2 (- x - 4)}{4 x - 12}$

Factor $4$ out of $4 x - 12$ .

Factor $4$ out of $4 x$ .

$f (x) = \frac{2 (- x - 4)}{4 (x) - 12}$

Factor $4$ out of $- 12$ .

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

Factor $4$ out of $4 x + 4 \cdot - 3$ .

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

Cancel the common factors.

Factor $2$ out of $4 (x - 3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

No holes