Question

вычислите 2/ 5+2√ 6 - 2/ 2√ 5-5

Answer 1

$frac{2}{5+2sqrt5}-frac{2}{2sqrt5-5}=frac{2(2sqrt5-5)-2(5+2sqrt5)}{(5+2sqrt5)(2sqrt5-5)}=$
$=frac{4sqrt{5}-10-10-4sqrt{5}}{(2sqrt5)^2-5^2}=frac{-20}{20-25}=frac{-20}{-5}=4$