Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -1}\frac{2 x^{2} - 10 x - 12}{8 x^{2} + 9 x + 1}$

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: $LaTeX: \lim_{x \to -1}\frac{2 x^{2} - 10 x - 12}{8 x^{2} + 9 x + 1} = \lim_{x \to -1}\frac{4 x - 10}{16 x + 9} = \frac{4 (-1) - 10}{16 (-1) + 9} = 2$