I am trying to solve $\displaystyle\lim_{x\to3^-}\frac{3}{x - 3} - \frac{3}{x} - 9$. Here's what I have tried.
$ \lim_{x\to3^-}\frac{3}{x - 3} - \frac{3}{x} - 9 \\ \lim_{x\to3^-}\frac{3x}{x(x - 3)} - \frac{3(x-3)}{x(x-3)} - \frac{9x(x-3)}{x(x-3)} \\ \lim_{x\to3^-}\frac{3x - 3x - 9x^2 + 27x}{x(x - 3)} \\ \lim_{x\to3^-}\frac{- 9x^2 + 27x}{x^2 - 3x)} \\ $
By L' Hopital's Rule,
$ \lim_{x\to3^-}\frac{-18x + 27}{2x - 3} \\ \lim_{x\to3^-}\frac{-18}{2} \\ -9 \\ $
However, Wolfram Alpha claims that the limit is infinity: http://www.wolframalpha.com/input/?i=lim+x+-%3E+3+%5Cfrac%7B3%7D%7Bx+-+3%7D+-+%5Cfrac%7B3%7D%7Bx%7D+-+9
Why?