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问题: 高一不等式问题

已知三角形ABC的三边长为a,b,c,且m为正数,求证 (a/a+m)+(b/b+m)>c/c+m

解答:

a/(a+m)+b/(b+m)>c/(c+m)?
c/(c+m)=1/(1+m/c)<1/(1+m/(a+b))=(a+b)/(a+b+m)=
=a/(a+b+m)+b/(a+b+m)<a/(a+m)+b/(b+m)