УПРОСТИТЕ ВЫРАЖЕНИЕ ( Х-У: Х - У-Х:У) : Х+У:ХУ

Question

УПРОСТИТЕ ВЫРАЖЕНИЕ ( Х-У: Х - У-Х:У) : Х+У:ХУ

Answer 1

( (x-y) / (x)  -  (y-x) / (y) ) / ( (x+y) / (yx) ) =
= ( (x-y) / (x)  -  (y-x) / (y) ) * ( (yx) / (x+y) ) =
= ( ( y(x-y) - x(y-x) ) / (xy) ) * ( (yx) / (x+y) ) =
= ( y(x-y) + x(x-y) ) / ( x+y ) = ( (y+x)(x-y) ) / ( x+y ) = x-y