令(y+z)/x=(z+x)/y=(x+y)/z=k
y+z=kx
x+z=ky
x+y=kz
2(x+y+z)=k(x+y+z)
2(x+y+z)=k(x+y+z)
(2-k)(x+y+z)=0(x+y+z≠ 0)
k=2
x+y=2z
(x+y-z)/(x+y+z)
=(2z-z)/(2z+z)
=z/3z
=1/3