Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -2}\frac{4 x^{2} + 44 x + 72}{3 x^{2} + 3 x - 6}$

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: $LaTeX: \lim_{x \to -2}\frac{4 x^{2} + 44 x + 72}{3 x^{2} + 3 x - 6} = \lim_{x \to -2}\frac{8 x + 44}{6 x + 3} = \frac{8 (-2) + 44}{6 (-2) + 3} = - \frac{28}{9}$