[(1/x)-(1/y)+(1/z)]xy/(xy+yz+zx)=
[(1/x)* xy-(1/y)* xy+(1/z)* xy]/(xy+yz+zx)=
(y - x + xy/z)/(xy+yz+zx)=
(y - x + xy/z) * z/(xy+yz+zx)*z =
( zy - zx + xy ) / z(xy+yz+zx)
[(1/x)-(1/y)+(1/z)]xy/(xy+yz+zx)=
[(1/x)* xy-(1/y)* xy+(1/z)* xy]/(xy+yz+zx)=
(y - x + xy/z)/(xy+yz+zx)=
(y - x + xy/z) * z/(xy+yz+zx)*z =
( zy - zx + xy ) / z(xy+yz+zx)