Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{3 x^{2} - 8 x + 1}{- 3 x^{2} + 6 x + 6}

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{3 x^{2} - 8 x + 1}{- 3 x^{2} + 6 x + 6} = \lim_{x \to \infty}\frac{6 x - 8}{6 - 6 x} = \lim_{x \to \infty}\frac{6}{-6} = -1