Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -5}\frac{5 x^{2} - 10 x - 175}{4 x^{2} + 22 x + 10}$

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: $LaTeX: \lim_{x \to -5}\frac{5 x^{2} - 10 x - 175}{4 x^{2} + 22 x + 10} = \lim_{x \to -5}\frac{10 x - 10}{8 x + 22} = \frac{10 (-5) - 10}{8 (-5) + 22} = \frac{10}{3}$