一道数学题,实在不懂,

题目

一道数学题,实在不懂,
(y+z-x)/x=(x+z-y)/y=(x+y-z)/z 求[(x+y)(y+z)]/xz的值（分数线用 / 代替）

答案

设(y+z-x)/x=(x+z-y)/y=(x+y-z)/z=k
{y+z-x=kx (1)
{x+z-y=ky (2)
{x+y-z=kz (3)
(1)+(2)+(3)得
x+y+z=k(x+y+z)
k=1或x+y+z=0
(1)+(2)得
2z=k(x+y) (4)
(2)+(3)得
2x=k(y+z) (5)
(4)×(5)得
4xz=k²(x+y)(y+z)
当k=1时
[(x+y)(y+z)]/xz=4/k²=4
当x+y+z=0时
[(x+y)(y+z)]/xz=(-z)(-x)/xz=-1