Question

设x>0,y.0,A=x+y/1+x+y,B=x/1+x=y/1+y,比较A,B大小

Answer 1

A=(x+y)/(1+x+y)=1-1/(1+x+y)

B=x/(1+x)+y/(1+y)=（x+2xy+y)/[(1+x)(1+y)

=（x+2xy+y)/(1+x+y+xy)=1-(1-xy)/(1+x+y+xy)

因为(1-xy)/(1+x+y+xy)A