Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 6 x^{2} - 4 x + 5}{- 4 x^{2} + 3 x + 1}

The limit is an indeterminate form of the type LaTeX: \displaystyle \frac{\infty}{\infty} . Using L'Hospitial's rule 2 times gives: LaTeX: \lim_{x \to -\infty}\frac{- 6 x^{2} - 4 x + 5}{- 4 x^{2} + 3 x + 1} = \lim_{x \to -\infty}\frac{- 12 x - 4}{3 - 8 x} = \lim_{x \to -\infty}\frac{-12}{-8} = \frac{3}{2}