Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -7}\frac{5 x^{2} + 80 x + 315}{7 x^{2} + 43 x - 42}$

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: $LaTeX: \lim_{x \to -7}\frac{5 x^{2} + 80 x + 315}{7 x^{2} + 43 x - 42} = \lim_{x \to -7}\frac{10 x + 80}{14 x + 43} = \frac{10 (-7) + 80}{14 (-7) + 43} = - \frac{2}{11}$