Verified answer

( x ÷ y + 1 ÷ 1 - y ÷ x ) ÷ x^2y + xy ÷ x^2y - xy^2

= [x/(y + 1) / (1 - y)/x] / [(x^2y + xy) / (x^2y - xy^2)]

= [x^2 / -(y^2 - 1)} / [xy(x + 1) / xy(x - y)]

= x^2(x - y) / -(x + 1)(y^2 - 1)

[( x÷y+1÷ 1− y÷x ) ÷ x^2y]+(xy÷x^2y)-xy^^2

=[( x/y + 1 - y/x ) / x^2y ] + 1/x - xy^2

= [ ( x^2/xy + xy/xy - y^2/xy / x^2y ] + 1/x - xy^2

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

= (x^2 + xy -y^2) / x^2y^3 + 1/x - xy^2