Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -7}\frac{3 x^{2} - 6 x - 189}{- 2 x^{2} - 16 x - 14}$

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: $LaTeX: \lim_{x \to -7}\frac{3 x^{2} - 6 x - 189}{- 2 x^{2} - 16 x - 14} = \lim_{x \to -7}\frac{6 x - 6}{- 4 x - 16} = \frac{6 (-7) - 6}{- 4 (-7) - 16} = -4$