Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -2}\frac{5 x^{2} + 25 x + 30}{8 x^{2} + 17 x + 2}$

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: $LaTeX: \lim_{x \to -2}\frac{5 x^{2} + 25 x + 30}{8 x^{2} + 17 x + 2} = \lim_{x \to -2}\frac{10 x + 25}{16 x + 17} = \frac{10 (-2) + 25}{16 (-2) + 17} = - \frac{1}{3}$