Question

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

Answer 1

`x=-1/4` and `x = 6/k` for integer `k`

Explanation:

`12x+3=0` at `x=-1/4`

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

`pi+(6pi)/x = kpi` for integer `k`

And that happens where `(6pi)/x = kpi` for integer `k`

Which is at `x = 6/k` for integer `k`