Question

Simplificando a expressão
$\frac{2 + \frac{1}{ \sqrt{2} } }{ \sqrt{2} - 1 }$
Obtemos?​

Answer 1

$\dfrac{2+\frac{1}{\sqrt{2}}}{\sqrt{2}-1}$

$\dfrac{\frac{2\sqrt{2}+1}{\sqrt{2}}}{\sqrt{2}-1}$

$\dfrac{2\sqrt{2}+1}{\sqrt{2}\cdot(\sqrt{2}-1)}$

$\dfrac{2\sqrt{2}+1}{2-\sqrt{2}}$

$\dfrac{2\sqrt{2}+1}{2-\sqrt{2}} \cdot \dfrac{2+\sqrt{2}}{2+\sqrt{2}}$

$\dfrac{4\sqrt{2}+4+2+\sqrt{2} }{4-2}$

$\boxed{\dfrac{5\sqrt{2}+6}{2}}$