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