(x^-1+y^-1)*2xy/x^2+2xy+y^2

Question

(x^-1+y^-1)*2xy/x^2+2xy+y^2

Answer 1

(х^2-y^2)^2 / (x^2+2xy+y^2)  :  ( (1/x)^2 - (1/y)^2 ) =
= (  (x+y)(x-y) )^2  / (x+y)^2   : ( (1/x)^2 - (1/y)^2 ) =
= ( (x+y)(x-y)(x+y)(x-y) )  / ( (x+y)(x+y) )  :  (y^2-x^2) / x^2y^2 == (x-y)(x-y)  *  (- x^2y^2 / (x^2-y^2) ) =
= (x-y)(x-y)  *  (- x^2y^2 /  ( (x+y)(x-y) ) = -x^2y^2(x-y) / (x+y)