Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -6}\frac{5 x^{2} + 20 x - 60}{- 5 x^{2} - 36 x - 36}$

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: $LaTeX: \lim_{x \to -6}\frac{5 x^{2} + 20 x - 60}{- 5 x^{2} - 36 x - 36} = \lim_{x \to -6}\frac{10 x + 20}{- 10 x - 36} = \frac{10 (-6) + 20}{- 10 (-6) - 36} = - \frac{5}{3}$