Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -6}\frac{3 x^{2} - 6 x - 144}{- 3 x^{2} - 17 x + 6}$

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: $LaTeX: \lim_{x \to -6}\frac{3 x^{2} - 6 x - 144}{- 3 x^{2} - 17 x + 6} = \lim_{x \to -6}\frac{6 x - 6}{- 6 x - 17} = \frac{6 (-6) - 6}{- 6 (-6) - 17} = - \frac{42}{19}$