Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -3}\frac{5 x^{2} - 15 x - 90}{8 x^{2} + 23 x - 3}$

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: $LaTeX: \lim_{x \to -3}\frac{5 x^{2} - 15 x - 90}{8 x^{2} + 23 x - 3} = \lim_{x \to -3}\frac{10 x - 15}{16 x + 23} = \frac{10 (-3) - 15}{16 (-3) + 23} = \frac{9}{5}$