化简:分式加减

题目

化简:分式加减
化简:(2x-y-z)/(x-y)(x-z)+(2y-z-x)/(y-z)(y-x)+(2z-y-x)/(z-y)(z-x)

答案

(2x-y-z)/(x-y)(x-z)+(2y-z-x)/(y-z)(y-x)+(2z-y-x)/(z-y)(z-x)
= (x-y+x-z)/(x-y)(x-z)+(y-z+y-x)/(y-z)(y-x)+(z-y+z-x)/(z-y)(z-x)
= (x-y)/(x-y)(x-z)+(x-z)/(x-y)(x-z)+
(y-z)/(y-z)(y-x)+(y-x)/(y-z)(y-x)+
(z-y)/(z-y)(z-x)+(z-x)/(z-y)(z-x)
= 1/(x-z)+1/(x-y)+1/(y-x)+1/(y-z)+1/(z-x)+1/(z-y)
= 1/(x-y)+1/(y-x)+1/(x-z)+1/(z-x)+1/(z-y)+1/(y-z)
=0