Question

СРОЧНО! упростите выражение (√2 - 1) / √5 - (2/√10)

Answer 1

$frac{sqrt2 - 1}{sqrt5 -frac{2}{sqrt{10}}}=frac{sqrt2 - 1}{frac{sqrt5*sqrt{10-}2}{sqrt{10}}}=frac{sqrt{10}(sqrt2-1)}{5sqrt2-2}=frac{(sqrt{20}-sqrt{10})(5sqrt2+2)}{46}=\ frac{8sqrt{10}+4sqrt5-10sqrt2}{46}=frac{4sqrt{10}+2sqrt5-5sqrt2}{23}$