Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 6}\frac{4 x^{2} + 4 x - 168}{6 x^{2} - 37 x + 6}$

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: $LaTeX: \lim_{x \to 6}\frac{4 x^{2} + 4 x - 168}{6 x^{2} - 37 x + 6} = \lim_{x \to 6}\frac{8 x + 4}{12 x - 37} = \frac{8 (6) + 4}{12 (6) - 37} = \frac{52}{35}$