令(x+y)/z=(y+z)/x=(x+z)/y=k

所以x+y=kz

y+z=kx

x+z=ky

相加

2(x+y+z)=k(x+y+z)

(x+y+z)(k-2)=0

若x+y+z=0,则x+y=-z

所以(x+y-2z)/(x+y+2z)

=-3z/z

=-3

若k-2=0,k=2

则x+y=kz=2z

所以(x+y-2z)/(x+y+2z)

=0/4z

=0

所以(x+y-2z)/(x+y+2z)=0或-3