n\frac{n-\sqrt{n^2+ 2n}}{n+\sqrt{n^2+ 2n}}=n\frac{n-\sqrt{n^2+ 2n}}{n+\sqrt{n^2+ 2n}}\frac{n+\sqrt{n^2+ 2n}}{n+\sqrt{n^2+ 2n}}=n\frac{-2n}{\left(n+\sqrt{n^2+ 2n}\right)^2}=\frac{-2n^2}{n^2+2n\sqrt{n^2+ 2n}+n^2+2n}=\frac{-2n^2}{n^2\left(1+\frac{2}{n}\sqrt{n^2+ 2n}+1+\frac{2}{n}\right)}=\frac{-2}{\left(1+2\sqrt{1+ \frac{2}{n}}+1+\frac{2}{n}\right)}