Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 3}\frac{4 x^{2} - 32 x + 60}{3 x^{2} - 3 x - 18}$

The limit is an indeterminate form of the type $LaTeX: \displaystyle \frac{0}{0}$ . Using L'Hospitial's rule and then the evaluation theorem gives: $LaTeX: \lim_{x \to 3}\frac{4 x^{2} - 32 x + 60}{3 x^{2} - 3 x - 18} = \lim_{x \to 3}\frac{8 x - 32}{6 x - 3} = \frac{8 (3) - 32}{6 (3) - 3} = - \frac{8}{15}$