z分之x+y等于y分之x+z等于x分之y+z(x+y+z不等于零)求x+y+z分之x+y-z的值

问题描述:

z分之x+y等于y分之x+z等于x分之y+z(x+y+z不等于零)求x+y+z分之x+y-z的值

根据等比性质,(x+y)/z=(x+z)/y=(y+z)/x=(2x+2y+2z)/(x+y+z)=2 (x+y+z≠0)
∴x+y=2z
∴(x+y-z)/(x+y+z)=(2z-z)/(2z+z)=1/3