Question

Simplificando a expressão obtemos

Answer 1

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

Racionalizando, temos:

$\frac{2\sqrt{2}~+~1}{2-\sqrt{2}}~.~\frac{2+\sqrt{2}}{2+\sqrt{2}}\\\\\\\frac{2\sqrt{2}~.~2~+~2\sqrt{2}~.~\sqrt{2}~+~1~.~2~+~1~.~\sqrt{2}}{2^2-\sqrt{2}^2}\\\\\\\frac{4\sqrt{2}~+~2~.~2~+~2~+\sqrt{2}}{2^2-\sqrt{2}^2}\\\\\\\frac{5\sqrt{2}~+~6}{4-2}\\\\\\\frac{5\sqrt{2}~+~6}{2}\\\\\\\frac{5\sqrt{2}}{2}+\frac{6}{2}\\\\\\\boxed{3+\frac{5\sqrt{2}}{2}}$

Resposta: Letra D