Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -4}\frac{2 x^{2} - 10 x - 72}{2 x^{2} + 17 x + 36}$

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: $LaTeX: \lim_{x \to -4}\frac{2 x^{2} - 10 x - 72}{2 x^{2} + 17 x + 36} = \lim_{x \to -4}\frac{4 x - 10}{4 x + 17} = \frac{4 (-4) - 10}{4 (-4) + 17} = -26$