Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 7}\frac{4 x^{2} - 4 x - 168}{- 5 x^{2} + 40 x - 35}$

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: $LaTeX: \lim_{x \to 7}\frac{4 x^{2} - 4 x - 168}{- 5 x^{2} + 40 x - 35} = \lim_{x \to 7}\frac{8 x - 4}{40 - 10 x} = \frac{8 (7) - 4}{40 - 10 (7)} = - \frac{26}{15}$