Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 6}\frac{2 x^{2} - 8 x - 24}{- x^{2} + 7 x - 6}$

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: $LaTeX: \lim_{x \to 6}\frac{2 x^{2} - 8 x - 24}{- x^{2} + 7 x - 6} = \lim_{x \to 6}\frac{4 x - 8}{7 - 2 x} = \frac{4 (6) - 8}{7 - 2 (6)} = - \frac{16}{5}$