Question

Efetuando 1$Efetuando \left \{ \frac{1}{ \sqrt{3-1} }+ \frac{1}{ \sqrt{3+1} } \left \}$

Answer 1

$\boxed{ \frac{1}{ \sqrt{3-1} } + \frac{1}{ \sqrt{3+1} }=\frac{1}{ \sqrt{2} }+\frac{1}{2}=\frac{2+ \sqrt{2} }{2 \sqrt{2} } .\frac{\sqrt{2} }{ \sqrt{2} }=\frac{2 \sqrt{2} +2}{4}=\frac{ \sqrt{2} +1}{2}}$

Answer 2

$\;\; \frac{1}{\sqrt{3-1}} + \frac{1}{\sqrt{3+1}} \\ =\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{4}}\\ =\frac{1}{\sqrt{2}} + \frac{1}{2}=\frac{2+\sqrt{2}}{2\sqrt{2}}\\ =\frac{2+\sqrt{2}}{2\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}= \frac{2\sqrt{2}+\sqrt{4}}{2\sqrt{4}} = \frac{2\sqrt{2}+2}{2\cdot2} = \frac{2(\sqrt{2}+1)}{2\cdot2}= \frac{\sqrt{2}+1}{2}$