The graph of y=(x^2-9)/(3x-9) has:

(sorry for not typing out the answer not related to my question)

a) a vertical asymptote at x=3

b)....

c) a removable discontinuity at x=3

d)...

e)...

I know the answer is c but I got confused with answer a.

Doesn't the graph of y=(x^2-9)/(3x-9) has a vertical asymptote at x=3 if numbers are plugged into the equation? How do we know if (x-3) should be factored out or not?

Thanks