Освобождения от иррациональности в знаменателе дроби 1) ( √x+√y)/(√x-√y)  2) (20-4√a)/(5√a-a) 3) (9√a+√b)/(9b+81√ab) 4) (x-a√x)/(√ax-a√a)

1)  (\sqrt{x}-\sqrt{y})/(\sqrt{x}+\sqrt{y})= (\sqrt{x}-\sqrt{y})(\sqrt{x}-\sqrt{y})/(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})= (x-2\sqrt{xy}+y)/(x-y) 2)  (20-4\sqrt{a})/(5\sqrt{a}-a)=4(5-\sqrt{a})/\sqrt{a}(5-\sqrt{a})=4\sqrt{a}/a 3) (9\sqrt{a}+\sqrt{b})/(9b+81\sqrt{ab})=(9\sqrt{a}+\sqrt{b})/(9\sqrt{b}(\sqrt{b}+9\sqrt{a})=\sqrt{b}/9b 4)  (x-a\sqrt{x})/(\sqrt{ax}-a\sqrt{a})=\sqrt{x}(\sqrt{x}-a)/\sqrt{a}(\sqrt{x}-a)=\sqrt{ax}/a

1) (√x+√y)/(√x-√y)= = (√x+√y)²/[(√x-√y)·( √x+√y)] = = (√x+√y)²/[(√x)²-(√y)²] = = (√x+√y)²/(x-y)   2) (20-4√a)/(5√a-a) = = 4(5 - √a)/(5√а - √a·√a) = 4(5 - √a)/[√a(5 -√a)] = = 4/√a = = 4√a/(√a·√a) = = 4√a/a   3) (9√a+√b)/(9b+81√ab) = = (9√a+√b)/[9√b(√b+9√a]) = = 1/(9√b) = = √b/(9b)   4) (x-a√x)/(√ax-a√a) = = √x(√x - a)/[√a(√x - a)] = = √x/√a = = √(ax)/a