Question

Сократить дробь$frac{5- sqrt{10} }{ sqrt{10}-2 }$

Answer 1

$frac{5- sqrt{10} }{ sqrt{10}-2 } = frac{ ( sqrt{5}) ^{2}- sqrt{5}* sqrt{2} }{ sqrt{5}* sqrt{2}- ( sqrt{2}) ^{2} } = frac{ sqrt{5} *( sqrt{5}- sqrt{2} )}{ sqrt{2}*( sqrt{5}- sqrt{2} ) } = frac{ sqrt{5} }{ sqrt{2} } = sqrt{ frac{5}{2} } = sqrt{2,5}$