What are the vertical asymptotes of the function f(x) = the quantity of 3x plus 9, all over x squared plus 4x minus 12?

In order to find the vertical asymptotes of a rational function you must set the denominator = 0 and solve for x.

If F(x) = (3x + 9) / (x^2 + 4x - 12), then set x^2 + 4x - 12 = 0 and solve for x.

(x + 6)(x - 2) = 0

x + 6 = 0 so then x = -6
x - 2 = 0 so then x = 2 

For this particular function, you have 2 vertical asymptotes.  x = -6 and x = 2