Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 2}\frac{4 x^{2} + 12 x - 40}{- 6 x^{2} + 11 x + 2}$

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: $LaTeX: \lim_{x \to 2}\frac{4 x^{2} + 12 x - 40}{- 6 x^{2} + 11 x + 2} = \lim_{x \to 2}\frac{8 x + 12}{11 - 12 x} = \frac{8 (2) + 12}{11 - 12 (2)} = - \frac{28}{13}$