$\mathop {\lim }\limits_{x \to -\infty }\frac{\sqrt{-x^3-2x+1}+4\sqrt{2-x}}{x^2-1}=\mathop {\lim }\limits_{x \to -\infty }\frac{\frac{1}{x^2}\sqrt{-x^3-2x+1}+\frac{4}{x^2}\sqrt{2-x}}{1-\frac{1}{x^2}}$ $=\mathop {\lim }\limits_{x \to -\infty }\frac{\sqrt{-\frac{1}{x}-\frac{2}{x^3}+\frac{1}{x^4}}+4\sqrt{\frac{2}{x^4}-\frac{1}{x^3}}}{1-\frac{1}{x^2}}$
$=\frac{\sqrt{0}+4.\sqrt{0}}{1-0}$
$=0$.