(x+y-xy)/(x+y+2xy)=(y+z-2yz)/(y+z+3yz)=(z+x-3zx)/(

问题补充：

(x+y-xy)/(x+y+2xy)=(y+z-2yz)/(y+z+3yz)=(z+x-3zx)/(z+x+4zx),且2/x=3/y=1/z,则xyz=?

答案：

设2/x=3/y=1/z为k

x=2k,y=3k,z=k

代入得1-k/1+2k=4-6k/4+9k=3-6k/3+8k

算出k得k=-1

x=-2,y=-3,z=-1

xyz=-6

======以下答案可供参考======

供参考答案1:

无解~~令2/x=3/y=1/z=1/t

则:x=2t,y=3t,z=t

代入方程分子分母同消去t得:

(5+6t)/(5+12t)=(4-6t)/(4+9t)=(3-6t)/(3+8t)

无解