$\lim_{n \to 2} \dfrac{2x-x^2}{x^3-x^2-3x+2}$
= $\lim_{n \to 2} \dfrac{-x(x-2)}{x^3-2x^2+x^2-2x-x+2}$
= $\lim_{n \to 2} \dfrac{-x(x-2)}{x^2(x-2)+x(x-2)-(x-2)}$
= $\lim_{n \to 2} \dfrac{-x(x-2)}{(x^2+x-1)(x-2)}$
= $\lim_{n \to 2} \dfrac{-x}{x^2+x-1}$
= $ \dfrac{-2}{2^2+2-1}$
= $ \dfrac{-2}{5}$