Introduction to Limits · Challenge problem

Cancel the common factor first, then use sign analysis to evaluate $\displaystyle\lim_{x\to2^{+}}\frac{x^{2}-3x+2}{x^{2}-4x+4}$ and $\displaystyle\lim_{x\to2^{-}}\frac{x^{2}-3x+2}{x^{2}-4x+4}$. Classify the discontinuity at $x=2$.