Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -2}\frac{4 x^{2} - 16 x - 48}{- 5 x^{2} - 7 x + 6}$

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: $LaTeX: \lim_{x \to -2}\frac{4 x^{2} - 16 x - 48}{- 5 x^{2} - 7 x + 6} = \lim_{x \to -2}\frac{8 x - 16}{- 10 x - 7} = \frac{8 (-2) - 16}{- 10 (-2) - 7} = - \frac{32}{13}$