Question

(√8-√6) / (√8+√6) - (√8+√6) / (√8-√6)

Answer 1

$\frac{ \sqrt{8}- \sqrt{6} }{ \sqrt{8} + \sqrt{6} } - \frac{ \sqrt{8}+ \sqrt{6} }{ \sqrt{8} - \sqrt{6} }= \frac{( \sqrt{8}- \sqrt{6} )*( \sqrt{8}- \sqrt{6} )-( \sqrt{8}+ \sqrt{6} )*( \sqrt{8}+ \sqrt{6} ) }{ (\sqrt{8} +\sqrt{6})(\sqrt{8} -\sqrt{6}) }=$

$\frac{(\sqrt{8}) ^{2} -2* \sqrt{8}* \sqrt{6} + (\sqrt{6} )^{2} -((\sqrt{8}) ^{2}+2* \sqrt{8}* \sqrt{6} + (\sqrt{6} )^{2})}{ (\sqrt{8}) ^{2} - (\sqrt{6} )^{2} } =$

$= \frac{8-2 \sqrt{48} +6-(8+2 \sqrt{48} +6)}{8-6} =\frac{8-2 \sqrt{48} +6-8-2 \sqrt{48} -6}{2}=$

$= \frac{-4 \sqrt{48} }{2} =-2 \sqrt{48} =-2 \sqrt{4*12} =-2*2 \sqrt{12} =-4 \sqrt{12}$