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

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: $LaTeX: \lim_{x \to -1}\frac{2 x^{2} + 12 x + 10}{- 2 x^{2} - 10 x - 8} = \lim_{x \to -1}\frac{4 x + 12}{- 4 x - 10} = \frac{4 (-1) + 12}{- 4 (-1) - 10} = - \frac{4}{3}$