Why does the criterion for to have a vertical asymptote at c require that q(c) = 0 but p...

Why does the criterion for to have a vertical asymptote at c require that q(c) = 0 but p(c) ≠ 0 (see page 170)? Why not just q(c) =0? Can you think of a rational function that does not have a vertical asymptote at a point where its denominator is zero? [Hint: Make both p(c) = 0 and q(c) = 0.]