Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{2 x^{2} - 5 x + 5}{7 x^{2} + 6 x + 9}

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{2 x^{2} - 5 x + 5}{7 x^{2} + 6 x + 9} = \lim_{x \to -\infty}\frac{4 x - 5}{14 x + 6} = \lim_{x \to -\infty}\frac{4}{14} = \frac{2}{7}