Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{7 x^{2} + 3 x - 6}{- 9 x^{2} - 3 x + 8}

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{7 x^{2} + 3 x - 6}{- 9 x^{2} - 3 x + 8} = \lim_{x \to \infty}\frac{14 x + 3}{- 18 x - 3} = \lim_{x \to \infty}\frac{14}{-18} = - \frac{7}{9}