放缩!不等式放缩法的极品难题!

题目

放缩!不等式放缩法的极品难题!
若x,y,z,a,b,c,r>0,证明:
(x+y+a+b）/（x+y+a+b+c+r)+（y+z+b+c)/(y+z+a+b+c+r)
>(x+z+a+c）/（x+z+a+b+c+r)
字母没错
放心做吧

答案

这个不等式不强.放缩两次仍成立.证明：(x+y+a+b)/(x+y+a+b+c+r)+(y+z+b+c)/(y+z+a+b+c+r)>(x+y+a+b)/(x+y+z+2a+b+c+r)+(y+z+b+c)/(x+y+z+2a+b+c+r)=(x+2y+z+a+2b+c)/(x+y+z+2a+b+c+r)>(x+y+z+a+b+c)/(x+y+z+2a+b+c+r...