Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -6}\frac{2 x^{2} + 8 x - 24}{- 8 x^{2} - 44 x + 24}$

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: $LaTeX: \lim_{x \to -6}\frac{2 x^{2} + 8 x - 24}{- 8 x^{2} - 44 x + 24} = \lim_{x \to -6}\frac{4 x + 8}{- 16 x - 44} = \frac{4 (-6) + 8}{- 16 (-6) - 44} = - \frac{4}{13}$