Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -2}\frac{3 x^{2} - 6 x - 24}{- 4 x^{2} - 17 x - 18}$

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: $LaTeX: \lim_{x \to -2}\frac{3 x^{2} - 6 x - 24}{- 4 x^{2} - 17 x - 18} = \lim_{x \to -2}\frac{6 x - 6}{- 8 x - 17} = \frac{6 (-2) - 6}{- 8 (-2) - 17} = 18$