Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 8}\frac{4 x^{2} - 4 x - 224}{9 x^{2} - 73 x + 8}$

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: $LaTeX: \lim_{x \to 8}\frac{4 x^{2} - 4 x - 224}{9 x^{2} - 73 x + 8} = \lim_{x \to 8}\frac{8 x - 4}{18 x - 73} = \frac{8 (8) - 4}{18 (8) - 73} = \frac{60}{71}$