(x^2-4x+6)(x-3)^-3

Answer 1

what about it?

(x^2-4x+6)/(x-3)^3
has asymptote at x=3

see graph and analysis at

http://www.wolframalpha.com/input/?i=%28x^2-4x%2B6%29%2F%28x-3%29^3

where you can play around with other functions as you will.