因为z=2-x-y,所以1/(xy+2z)=1/(xy+4-2x-2y)=1/(x-2)(y-2)同理1/(yz+2x)=1/(y-2)(z-2)；1/(zx+2y)=1/(z-2)(x-2)再设r=x-2,s=y-2,t=z-2题目变为求1/rs+1/st+1/rt=(r+s+t)/rst而题中三个已知条件变为(r+2)(s+2)(t+2)=1...