Question

Simplificando a expressão $\frac{\sqrt{2} }{\sqrt{2}-1} -\frac{1}{\sqrt{2}}-\frac{3}{1+\sqrt{2} }$, vamos obter:

a)$\frac{-5\sqrt{2}+10 }{2}$

b)$7\sqrt{2} +2$

c)$5\sqrt{2} -15$

d)$\frac{\sqrt{2}+3 }{6}$

e)$\frac{7\sqrt{2}+1 }{2}$
Resposta com Cálculos por favor

Answer 1

Resposta:

Letra A

Explicação passo a passo:

$mmc=\sqrt{2} (\sqrt{2} -1)(\sqrt{2} +1)\\ \\ \\ \dfrac{\sqrt{2} .\sqrt{2} (\sqrt{2} +1)-(\sqrt{2} -1)(\sqrt{2} +1)-3\sqrt{2} (\sqrt{2} +1)}{\sqrt{2} (\sqrt{2} -1)(\sqrt{2} +1)}=\\ \\ \\ \dfrac{2(\sqrt{2} +1)-(\sqrt{2^2} -1^2)-3\sqrt{4} +3\sqrt{2} }{(\sqrt{2^2} -1^2)\sqrt{2} }=\\ \\ \\ \dfrac{2\sqrt{2} +2-(2-1)-3.(2)+3\sqrt{2} }{(2-1)\sqrt{2} }=\\ \\ \\ \dfrac{2\sqrt{2} +2-1-6+3\sqrt{2}}{\sqrt{2} }=\\ \\ \\ \dfrac{-5+5\sqrt{2} }{\sqrt{2} }=$

Racionalizar com √2 fator racionalizante

$\dfrac{\sqrt{2} .(-5+5\sqrt{2} }{\sqrt{2} .\sqrt{2} }=\\ \\ \\\boxed{ \dfrac{-5\sqrt{2} +10}{2}}$