`1/[x(x-y)(x-z)]+1/[y(y-z)(y-x)]+1/[z(z-x)(z-y)]`
`=(-1)/[x(x-y)(z-x)]+(-1)/[y(y-z)(x-y)]+(-1)/[z(z-x)(y-z)]`
`=-[yz(y-z)]/[xyz(x-y)(y-z)(z-x)]+[xz(z-x)]/[xyz(x-y)(y-z)(z-x)]+[xy(x-y)]/[xyz(x-y)(y-z)(z-x)]`
`=-(y^2z-yz^2+xz^2-x^2z+x^2y-xy^2)/[xyz(x-y)(y-z)(z-x)`
`=-(xy(x-y)-yz(x-y)-yz(z-x)+xz(z-x)]/[xyz(x-y)(y-z)(z-x)]`
`=-[y(x-y)(x-z)-z(z-x)(y-x)]/[xyz(x-y)(y-z)(z-x)]`
`=-[(x-y)(y-z)(x-z)]/[xyz(x-y)(y-z)(z-x)]`
`=1/(xyz)`
