\input amstex

$$\aligned
\frac{1}{x\,(x-y)\,(x-z)}-\frac{1}{y\,(z-y)\,(y-x)}+\frac{1}{z\,(z-x)\,(z-y)}&=\frac{1}{xyz}\qquad\bigg/\!\cdot xyz(x-y)(x-z)(y-z)\cr
y\,z\,(y-z)-x\,z\,(x-z)+x\,y\,(x-y)&=(x-y)(x-z)(y-z)\cr
y^2z-yz^2-x^2z+xz^2+x^2y-xy^2&=(x^2-xy-xz+yz)(y-z)=x^2y-x^2z-xy^2+xyz-xyz+xz^2+y^2z-yz^2\cr
0&=0
\endaligned$$
\bye