Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 6}\frac{5 x^{2} + 5 x - 210}{- 3 x^{2} + 20 x - 12}$

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: $LaTeX: \lim_{x \to 6}\frac{5 x^{2} + 5 x - 210}{- 3 x^{2} + 20 x - 12} = \lim_{x \to 6}\frac{10 x + 5}{20 - 6 x} = \frac{10 (6) + 5}{20 - 6 (6)} = - \frac{65}{16}$