Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -5}\frac{4 x^{2} + 48 x + 140}{7 x^{2} + 44 x + 45}$

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: $LaTeX: \lim_{x \to -5}\frac{4 x^{2} + 48 x + 140}{7 x^{2} + 44 x + 45} = \lim_{x \to -5}\frac{8 x + 48}{14 x + 44} = \frac{8 (-5) + 48}{14 (-5) + 44} = - \frac{4}{13}$