Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 6}\frac{4 x^{2} - 36 x + 72}{9 x^{2} - 51 x - 18}$

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: $LaTeX: \lim_{x \to 6}\frac{4 x^{2} - 36 x + 72}{9 x^{2} - 51 x - 18} = \lim_{x \to 6}\frac{8 x - 36}{18 x - 51} = \frac{8 (6) - 36}{18 (6) - 51} = \frac{4}{19}$