a,b,m∈R+ 且a

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a,b,m∈R+且aa,b,m∈R+且aa,b,m∈R+且aa1/a>1/bm/a>m/b1+m/a>1+m/b(a+m)/a>(b+m)/ba/(a+m)比较它们的倒数就可以了,知a/a+m∵a∴a

a,b,m∈R+ 且a
a,b,m∈R+ 且a

a,b,m∈R+ 且a
a1/a>1/b
m/a>m/b
1+m/a>1+m/b
(a+m)/a>(b+m)/b
a/(a+m)

比较它们的倒数就可以了,
知a/a+m

∵a∴a+m∵a,b,m∈R+,
有a+m>0,b+m>0,
∴1/(b+m)<1/(a+m),
∴-1/(a+m)<-1/(b+m),1-1/(a+m)<1-1/(b+m),
即a/(a+m)

a/(a+m)=1-m/(a+m)
b/(b+m)=1-m/(b+m)