Сократите дробь: 1)х√х-у√у/√х-√у 2)√а+√в/а√а+в√в 3)2√2-х√х/2+√2х+х

1) (х√х - у√у)/(√х - √у) = ((х√х - у√у) * (√х + √у))/((√х - √у) * (√х + √у)) =

= (x^2 - у√(у * x) + x√(у * x) – y^2)/(x – y) = ((x – y) * (x + y) + √(у * x) * (x – y))/(x – y) =

= (x – y) * (x + y + √(у * x))/(x – y) = x + y + √(у * x).

2) (√а + √b)/(а√а + b√b) = ((√а + √b) * (√а - √b))/((а√а + b√b) * (√а - √b)) =

= (a – b)/(a^2 + b√(a * b) - a√(a * b) – b^2) = (a – b)/((a – b) * (a + b) - √(a * b) * (a – b)) =

= (a – b)/((a – b) * (a + b - √(a * b))) = 1/(a + b - √(a * b)).

3) (2√2 - х√х)/(2 + √2х + х) = ((2√2 - х√х) * (√2 + √х))/((2 + √2х + х) * (√2 + √х)) =

= (4 - x√(2 * х) + 2√(2 * х) – x^2)/((2 + √2х + х) * (√2 + √х)) =

= ((2 – x) * (2 + x) + √(2 * х) * (2 – x))/((2 + √2х + х) * (√2 + √х)) =

= ((2 – x) * (2 + x + √(2 * х)))/((2 + √2х + х) * (√2 + √х)) = ((√2 + √х) * (√2 - √х))/(√2 + √х)

= √2 - √х.