Question

Urgent!Calculati: $\frac{4}{2+ \sqrt{2} } -5+2 \sqrt{2}$

Answer 1

$\displaystyle \frac{4}{2+ \sqrt{2}} -5+2 \sqrt{2} = \frac{4\left(2- \sqrt{2} \right)}{4-2} -5+2 \sqrt{2} = \frac{4\left(2- \sqrt{2}\right) }{2} -5+2 \sqrt{2} = \\ \\ =2(2- \sqrt{2} )-5+2 \sqrt{2} =4-2 \sqrt{2} -5+2 \sqrt{2} =4-5=-1$