已知y+z分之x=z+x分之y=x+y分之z（x+y+z≠0）求x-y+z分之x+2y+z的值

题目

已知y+z分之x=z+x分之y=x+y分之z（x+y+z≠0）求x-y+z分之x+2y+z的值

答案

设：X/(Y+Z)=Y/(Z+X)=Z/(X+Y)=KK*(Y+Z)=XK*(Z+X)=YK*(X+Y)=ZK*(Y+Z+Z+X+X+Y)=X+Y+Z2K*(X+Y+Z)=X+Y+Z（x+y+z≠0）,K=1/2,K*(Z+X)=Y,X+Z=2Yx-y+z=2Y-Y=Yx+2y+z=2Y+2Y=4Yx-y+z分之x+2y+z=4Y/Y=4