Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 5}\frac{4 x^{2} + 8 x - 140}{- 3 x^{2} + 6 x + 45}$

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: $LaTeX: \lim_{x \to 5}\frac{4 x^{2} + 8 x - 140}{- 3 x^{2} + 6 x + 45} = \lim_{x \to 5}\frac{8 x + 8}{6 - 6 x} = \frac{8 (5) + 8}{6 - 6 (5)} = -2$