Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 1}\frac{2 x^{2} - 12 x + 10}{- 8 x^{2} + 6 x + 2}$

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: $LaTeX: \lim_{x \to 1}\frac{2 x^{2} - 12 x + 10}{- 8 x^{2} + 6 x + 2} = \lim_{x \to 1}\frac{4 x - 12}{6 - 16 x} = \frac{4 (1) - 12}{6 - 16 (1)} = \frac{4}{5}$