# For what values of x, if any, does f(x) = 1/((12x+3)sin(pi+(6pi)/x)  have vertical asymptotes?

Aug 7, 2017

$x = - \frac{1}{4}$ and $x = \frac{6}{k}$ for integer $k$

#### Explanation:

$12 x + 3 = 0$ at $x = - \frac{1}{4}$

sin(pi+(6pi)/x) = 0# where

$\pi + \frac{6 \pi}{x} = k \pi$ for integer $k$

And that happens where $\frac{6 \pi}{x} = k \pi$ for integer $k$

Which is at $x = \frac{6}{k}$ for integer $k$