State the vertical asymptote of the rational function ... f (x) = quantity x minus six times quantity x plus six divided by quantity x squared minus nine.

The equation is f (x) = (x-6 * (x+6)) / (x^2 - 9).

For the vertical asymptote test in a rational function. The denominator is first set to zero.

x^2 - 9 = 0

x^2 = 9

x = + - 3

The values for x are then substituted to the numerator.

x=3; x-6 (x+6) = 3-6 (3+6) = - 51

x=-3; x-6 (x+6) = - 3-6 (-3+6) = - 21

The zeros of the denominator do not make the numerator zero so the vertical asymptotes are x = + - 3