Evaluate the limit LaTeX: \displaystyle \lim_{x \to -5}\frac{5 x^{2} - 5 x - 150}{5 x^{2} + 32 x + 35}

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} - 5 x - 150}{5 x^{2} + 32 x + 35} = \lim_{x \to -5}\frac{10 x - 5}{10 x + 32} = \frac{10 (-5) - 5}{10 (-5) + 32} = \frac{55}{18}