Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -3}\frac{4 x^{2} + 28 x + 48}{4 x^{2} + 5 x - 21}$

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: $LaTeX: \lim_{x \to -3}\frac{4 x^{2} + 28 x + 48}{4 x^{2} + 5 x - 21} = \lim_{x \to -3}\frac{8 x + 28}{8 x + 5} = \frac{8 (-3) + 28}{8 (-3) + 5} = - \frac{4}{19}$