已知z分之(x+y)=x分之(y+z)=y分之(x+z)=k,(x+y+z≠0).求(x+y+z)分之(x+y-z)的值.要具体过程!

问题描述:

已知z分之(x+y)=x分之(y+z)=y分之(x+z)=k,(x+y+z≠0).求(x+y+z)分之(x+y-z)的值.要具体过程!

(x+y)/z =(y+z)/x = (x+z)/y = k ==> (x+y) = kz
(x+y-z)/(x+y+z)
=(kz-z)/(kz+z)
=(k-1)/(k+1)