Question

como eu resolvo está conta?

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Answer 1

Explicação passo-a-passo:

$= \frac{1 + \sqrt{3} }{ \sqrt{2} + 1 } \div \frac{1 - \sqrt{3} }{ \sqrt{2} - 1 }$

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

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

$= ( \frac{1 + \sqrt{3} }{1 - \sqrt{3} } . \frac{ \sqrt{2} - 1}{ \sqrt{2} + 1 } )( \frac{1 + \sqrt{3} }{1 + \sqrt{3} } )( \frac{ \sqrt{2} - 1 }{ \sqrt{2} - 1} )$

$= ( \frac{(1 + \sqrt{3} {)}^{2} }{(1 - \sqrt{3} )(1 + \sqrt{3}) } )( \frac{( \sqrt{2} - 1 {)}^{2} }{( \sqrt{2} + 1)( \sqrt{2} - 1) } )$

$= ( \frac{1 + 2 \sqrt{3} + 3}{1 - 3} )( \frac{2 - 2 \sqrt{2} + 1 }{2 - 1} )$

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

$= ( - 2 - \sqrt{3} )(3 - 2 \sqrt{2} )$

$= - 6 + 4 \sqrt{2} - 3 \sqrt{3} + 2 \sqrt{2} \sqrt{3}$

$= - 6 + 4 \sqrt{2} - 3 \sqrt{3} + 2 \sqrt{6}$