Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 3}\frac{4 x^{2} + 20 x - 96}{- 6 x^{2} + 20 x - 6}$

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: $LaTeX: \lim_{x \to 3}\frac{4 x^{2} + 20 x - 96}{- 6 x^{2} + 20 x - 6} = \lim_{x \to 3}\frac{8 x + 20}{20 - 12 x} = \frac{8 (3) + 20}{20 - 12 (3)} = - \frac{11}{4}$