因为x/y+z + y/z+x +z/x+y=1
所以x/y+z=1-y/z+x-z/x+y,两边同乘以x
得x^2/y+z=x-xy/z+x-xz/x+y
同理y^2/x+z=y-xy/z+y-yz/x+y,z^2=z-xz/y+z-yz/x+z
所以原式=x+y+z-(xy+zy)/x+z-(xz+yz)/x+y-(yx+zx)/y+z
=x+y+z-y-z-x
=0