Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 8}\frac{3 x^{2} - 33 x + 72}{- 7 x^{2} + 60 x - 32}$

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: $LaTeX: \lim_{x \to 8}\frac{3 x^{2} - 33 x + 72}{- 7 x^{2} + 60 x - 32} = \lim_{x \to 8}\frac{6 x - 33}{60 - 14 x} = \frac{6 (8) - 33}{60 - 14 (8)} = - \frac{15}{52}$