# For what values of x, if any, does f(x) = 1/((x-4)(x-7))  have vertical asymptotes?

Apr 14, 2016

$x = 4 \mathmr{and} x = 7$

#### Explanation:

Vertical asymptotes: $x - 4 = 0 \mathmr{and} x - 7 = 0$

=> $x = 4 \mathmr{and} x = 7$

${\lim}_{x \to 4} \frac{1}{\left(x - 4\right) \left(x - 7\right)} = \frac{1}{0 \cdot - 3} = \frac{1}{0} = \infty$

${\lim}_{x \to 7} \frac{1}{\left(x - 4\right) \left(x - 7\right)} = \frac{1}{3 \cdot 0} = \frac{1}{0} = \infty$