令(x+y)/z=(y+z)/x=(x+z)/y =k
x+y=kz
y+z=kx
x+z=ky
以上等式相加得
2(x+y+z)=k(x+y+z)
2(x+y+z)-k(x+y+z)=0
(2-k)(x+y+z)=0
k=2,或x+y+z=0
当k=2时
x+y=kz
x+y=2z
(x+y-z)/(x+y+3z)
=(2z-z)/(2z+3z)
=z/5z
=1/5
当x+y+z=0时
x+y=-z
(x+y-z)/(x+y+3z)
=(-z-z)/(-z+3z)
=0/2z
=0
综上（x+y-z)/(x+y+3z)=0或（x+y-z)/(x+y+3z)=1/5