Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -6}\frac{3 x^{2} + 12 x - 36}{- 3 x^{2} - 16 x + 12}$

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: $LaTeX: \lim_{x \to -6}\frac{3 x^{2} + 12 x - 36}{- 3 x^{2} - 16 x + 12} = \lim_{x \to -6}\frac{6 x + 12}{- 6 x - 16} = \frac{6 (-6) + 12}{- 6 (-6) - 16} = - \frac{6}{5}$