=$\frac{2x^{2}+2x+2x\sqrt{x^{2}+2x}-4x^{2}-4x}{\sqrt{x^2+2x}+2\sqrt{x^2+x}+x}$
=2x$\frac{\sqrt{x^2+2x}-x-1}{\sqrt{x^2+2x}+2\sqrt{x^2+x}+x}$
= $\lim_{x \to +\infty} $ = $\lim_{x \to +\infty} $ $\frac{-2}{(\sqrt{1+\frac{2}{x}}+2\sqrt{1+\frac{1}{x}}+1)(\sqrt{1+\frac{2}{x}}+1+\frac{1}{x}}$ $\frac{-2x}{(\sqrt{x^2+2x}+2\sqrt{x^2+x}+x)(\sqrt{x^2+2x}+x+1)}$ =$\frac{1}{4}$
