Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 9}\frac{2 x^{2} - 2 x - 144}{5 x^{2} - 49 x + 36}$

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: $LaTeX: \lim_{x \to 9}\frac{2 x^{2} - 2 x - 144}{5 x^{2} - 49 x + 36} = \lim_{x \to 9}\frac{4 x - 2}{10 x - 49} = \frac{4 (9) - 2}{10 (9) - 49} = \frac{34}{41}$