Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 8}\frac{2 x^{2} - 6 x - 80}{6 x^{2} - 52 x + 32}$

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: $LaTeX: \lim_{x \to 8}\frac{2 x^{2} - 6 x - 80}{6 x^{2} - 52 x + 32} = \lim_{x \to 8}\frac{4 x - 6}{12 x - 52} = \frac{4 (8) - 6}{12 (8) - 52} = \frac{13}{22}$