若xy-z不等于0,且(y+x)/x=(z+x)/y=(y+x)/z,求[(y+z)(z+x)(x+y)]/xyz的值?

设(y+z)/x=(z+x)/y=(y+x)/z=k
则y+z=kx, z+x=ky, y+x=kz
三式相加2(x+y+z)=k(x+y+z)
故当x+y+z=0时,k=-1, 但xy-z不等于0,可知x+y+z不等于0
故x+y+z不等于0,则k=2
[(y+z)(z+x)(x+y)]/xyz=(y+z)/x*(z+x)/y*(x+y)/z=k^3=8