Identify the vertical asymptotes of f(x) = quantity x plus 6 over quantity x squared minus 9x plus 18

f(x)  =      x + 6                      x + 6
          ------------------    =  -----------------
          x^2 - 9x + 18         (x - 6)(x - 3)

Vertical asymptotes occur when the denominator = zero

so here they are   x = 6 and x = 3 (both of these makes the above denominator = zero)