[tex]\frac{3}{\sqrt2+2}+\frac{4}{2\sqrt2-1}-\frac{5}{\sqrt2}=\\\\\frac{3}{\sqrt2+2}\cdot\frac{\sqrt2-2}{\sqrt2-2}+\frac{4}{2\sqrt2-1}\cdot\frac{2\sqrt2+1}{2\sqrt2+1}-\frac{5}{\sqrt2}\cdot\frac{\sqrt2}{\sqrt2}=\\\\\frac{3\sqrt2-6}{2-4}+\frac{8\sqrt2+4}{8-1}-\frac{5\sqrt2}{2}=\\\\\frac{3\sqrt2-6}{-2}+\frac{8\sqrt2+4}{7}-\frac{5\sqrt2}{2}=\\\\\frac{-3\sqrt2+6-5\sqrt2}{2}+\frac{8\sqrt2+4}{7}=\\\\\frac{-8\sqrt2+6}{2}+\frac{8\sqrt2+4}{7}=\\\\\frac{-56\sqrt2+42}{14}+\frac{16\sqrt2+8}{14}=[/tex]
[tex]\frac{-56\sqrt2+42+16\sqrt2+8}{14}=\frac{-40\sqrt2+50}{14}=\frac{2(-20\sqrt2+25)}{14}=\frac{-20\sqrt2+25}{7}[/tex]
