Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 5}\frac{4 x^{2} - 4 x - 80}{- 8 x^{2} + 45 x - 25}$

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: $LaTeX: \lim_{x \to 5}\frac{4 x^{2} - 4 x - 80}{- 8 x^{2} + 45 x - 25} = \lim_{x \to 5}\frac{8 x - 4}{45 - 16 x} = \frac{8 (5) - 4}{45 - 16 (5)} = - \frac{36}{35}$