Question

2 + √2
--------- = ???????
√2 + 1

Answer 1

Basta multiplicar pelo conjugado:

$\frac{2 + \sqrt{2} }{ \sqrt{2} + 1} . \frac{ \sqrt{2} - 1 }{ \sqrt{2} -1} = \frac{2 \sqrt{2}-2 +2 - \sqrt{2} }{2 -1} = \sqrt{2}$

Answer 2

multiplico pelo seu conjugado. 

$\frac{2+ \sqrt{2} }{ \sqrt{2} +1} . \frac{\sqrt{2}-1}{\sqrt{2}-1} \\\\\\= \frac{(2+\sqrt{2}).(\sqrt{2}-1)}{(\sqrt{2}+1).(\sqrt{2}-1)} \\\\\\= \frac{2\sqrt{2}-2+(\sqrt{2})^{2}-\sqrt{2}}{(\sqrt{2})^{2}-1^{2}} \\\\\\= \frac{2 \sqrt{2} +2-2- \sqrt{2} }{2-1} \\\\\\= \frac{2 \sqrt{2} - \sqrt{2} }{1} \\\\\\= \boxed{\boxed{\sqrt{2} }}$