Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -3}\frac{4 x^{2} - 12 x - 72}{8 x^{2} + 22 x - 6}$

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: $LaTeX: \lim_{x \to -3}\frac{4 x^{2} - 12 x - 72}{8 x^{2} + 22 x - 6} = \lim_{x \to -3}\frac{8 x - 12}{16 x + 22} = \frac{8 (-3) - 12}{16 (-3) + 22} = \frac{18}{13}$