Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 6}\frac{4 x^{2} - 32 x + 48}{- 6 x^{2} + 32 x + 24}$

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: $LaTeX: \lim_{x \to 6}\frac{4 x^{2} - 32 x + 48}{- 6 x^{2} + 32 x + 24} = \lim_{x \to 6}\frac{8 x - 32}{32 - 12 x} = \frac{8 (6) - 32}{32 - 12 (6)} = - \frac{2}{5}$