Consider the function f (x) = (x-9) / (x^3-81x)

Find the vertical asymptote (s) of f (x)

Well, here's a harder one

Basically, to find a vertical asymptote, we set the denominator to 0. Like this:

x^3 - 81x = 0

Then we solve for x.

x (x^2 - 81) = 0

x (x+9) (x-9) = 0

x = 0, 9, - 9

There are vertical asymptotes at x = 0, x = 9, and x = - 9.