Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -6}\frac{2 x^{2} - 4 x - 96}{9 x^{2} + 49 x - 30}$

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: $LaTeX: \lim_{x \to -6}\frac{2 x^{2} - 4 x - 96}{9 x^{2} + 49 x - 30} = \lim_{x \to -6}\frac{4 x - 4}{18 x + 49} = \frac{4 (-6) - 4}{18 (-6) + 49} = \frac{28}{59}$