Question

Решите:
\frac{\sqrt{2} +1}{\sqrt{2} - 1 } + \frac{\sqrt{2} -1}{\sqrt{2} + 1 } - \frac{\sqrt{2} +3}{\sqrt{2} }

Answer 1

$\frac{\sqrt{2} +1}{\sqrt{2} - 1 } + \frac{\sqrt{2} -1}{\sqrt{2} + 1 } - \frac{\sqrt{2} +3}{\sqrt{2} }=\frac{(\sqrt{2} +1)^2+(\sqrt{2} -1)^2}{(\sqrt{2} + 1 )(\sqrt{2} - 1)} - \frac{\sqrt{2} +3}{\sqrt{2} }=\frac{2+2\sqrt{2}+1+2-2\sqrt{2}+1}{(\sqrt{2})^2-1^2} - \frac{\sqrt{2} +3}{\sqrt{2} }=6-\frac{\sqrt{2} +3}{\sqrt{2} }=6-(\frac{\sqrt{2}}{\sqrt{2} }+\frac{3}{\sqrt{2} })=5-\frac{3}{\sqrt{2} }$