Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -7}\frac{4 x^{2} - 8 x - 252}{- 3 x^{2} - 15 x + 42}$

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: $LaTeX: \lim_{x \to -7}\frac{4 x^{2} - 8 x - 252}{- 3 x^{2} - 15 x + 42} = \lim_{x \to -7}\frac{8 x - 8}{- 6 x - 15} = \frac{8 (-7) - 8}{- 6 (-7) - 15} = - \frac{64}{27}$