已知：(x+y-z)/z=(x-y+z)/y+(y+z-x)/x,且xyz≠0,求代数式[(x+y)(y+z)(x+z)]/xyz的值

设x+y-z/z=x-y+z/y=y+z-x/x=k有x+y-z=kzx-y+z=kyy+z-x=kx三式相加得x+y+z=k（x+y+z） k=1 得x+y=（k+1）zx+z=（k+1）yy+z=（k+1）x当x+y+z≠0时(x+y)(y+z)(x+z)/xyz=（k+1）^3xyz/xyz=(k+1)^3=8当x+y+z=0时x+y=-z,x+...