Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -1}\frac{4 x^{2} - 4 x - 8}{- 6 x^{2} - 10 x - 4}$

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