2 \sqrt{2} - \frac{ \sqrt{2}+1 }{ \sqrt{2} -1}=2\sqrt2-\frac{(\sqrt2+1)(\sqrt2+1)}{(\sqrt2-1)(\sqrt2+1)}=2\sqrt2-\frac{(\sqrt2+1)^2}{(\sqrt2)^2-1}=
=2\sqrt2-\frac{2+2\sqrt2+1}{2-1}=2\sqrt2-\frac{3+2\sqrt2}{1}=
=2\sqrt2-(3+2\sqrt2)=2\sqrt2-3-2\sqrt2=-3