Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -7}\frac{3 x^{2} + 6 x - 105}{2 x^{2} + 22 x + 56}$

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: $LaTeX: \lim_{x \to -7}\frac{3 x^{2} + 6 x - 105}{2 x^{2} + 22 x + 56} = \lim_{x \to -7}\frac{6 x + 6}{4 x + 22} = \frac{6 (-7) + 6}{4 (-7) + 22} = 6$