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
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
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