Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 3}\frac{2 x^{2} - 4 x - 6}{- 3 x^{2} + 17 x - 24}$

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: $LaTeX: \lim_{x \to 3}\frac{2 x^{2} - 4 x - 6}{- 3 x^{2} + 17 x - 24} = \lim_{x \to 3}\frac{4 x - 4}{17 - 6 x} = \frac{4 (3) - 4}{17 - 6 (3)} = -8$