Освободите от иррациональности в знаменателе дроби 4/√10+√2

[tex] \frac{4}{ \sqrt{10}+ \sqrt{2} }* \frac{( \sqrt{10}- \sqrt{2} ) }{ (\sqrt{10} - \sqrt{2} )} = \\ \frac{4 \sqrt{10}-4 \sqrt{2} }{10-2} = \frac{4( \sqrt{10}- \sqrt{2} }{8} = \frac{ \sqrt{10}- \sqrt{2} }{2} [/tex]

[tex] \frac{4}{\sqrt{10} + \sqrt{2} } = \frac{4(\sqrt{10} - \sqrt{2})}{(\sqrt{10} + \sqrt{2})(\sqrt{10} - \sqrt{2}) }= \frac{4(\sqrt{10} - \sqrt{2})}{(\sqrt{10} )^{2} -( \sqrt{2})^{2} }= \frac{4(\sqrt{10} - \sqrt{2})}{10-2 }= \frac{4(\sqrt{10} - \sqrt{2})}{8} }[/tex][tex]= \frac{\sqrt{10} - \sqrt{2}}{2} }[/tex]