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