Question

((2/√2)+(1/√3))÷((1/√2)-(2/√3)) "passo a passo para chegar nesse resultado: -2-√6 "

Answer 1

Segue o passo a passo :)

$\frac{ \frac{2}{ \sqrt{2} } + \frac{1}{ \sqrt{3} } }{ \frac{1}{ \sqrt{2} } - \frac{2}{ \sqrt{3} } } \\ \\ \frac{ \frac{2 \sqrt{3}+ \sqrt{2} }{ \sqrt{2} \sqrt{3} } }{ \frac{ \sqrt{3} -2 \sqrt{2} }{ \sqrt{2} \sqrt{3} } } \\ \\ \frac{2 \sqrt{3}+ \sqrt{2}}{\sqrt{2} \sqrt{3} } . \frac{ \sqrt{2} \sqrt{3} }{\sqrt{3} -2 \sqrt{2} }= \frac{2 \sqrt{3}+ \sqrt{2}}{\sqrt{3} -2 \sqrt{2}} \\ \\ Racionalizando$
$\frac{(2 \sqrt{3}+ \sqrt{2})}{(\sqrt{3} -2 \sqrt{2})} .\frac{(\sqrt{3} +2 \sqrt{2})}{(\sqrt{3} +2 \sqrt{2})} = \frac{2 (\sqrt{3})^2+4 \sqrt{6}+ \sqrt{6}+2 (\sqrt{2})^2 }{ (\sqrt{3})^2+2 \sqrt{6}-2 \sqrt{6}-(2 \sqrt{2})^2 }= \frac{2*3+5 \sqrt{6}+2*2 }{3-4*2}= \frac{10+5 \sqrt{6} }{-5}= \\ \\ \\ \\ - \frac{5(2+ \sqrt{6} )}{5} =-(2+ \sqrt{6})=-2- \sqrt{6}$