Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -7}\frac{5 x^{2} + 20 x - 105}{9 x^{2} + 57 x - 42}$

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: $LaTeX: \lim_{x \to -7}\frac{5 x^{2} + 20 x - 105}{9 x^{2} + 57 x - 42} = \lim_{x \to -7}\frac{10 x + 20}{18 x + 57} = \frac{10 (-7) + 20}{18 (-7) + 57} = \frac{50}{69}$