若a=y+1/x-y,b=y/x,如果x>y>0,那么a与b的大小关系是?

题目

若a=y+1/x-y,b=y/x,如果x>y>0,那么a与b的大小关系是?

答案

a-b
=(y+1)/(x-y)-y/x
=[x(y+1)-y(x-y)]/[x(x-y)]
=(xy+x-xy+y²)/[x(x-y)]
=(x+y²)/[x(x-y)]
x>y>0
x-y>0 x>0 x+y²>0
(x+y²)/[x(x-y)]>0
a-b>0
a>b