考虑函数f(x)＝x/(1＋x)＝1－1/(1＋x)
易知,当x＞0时,f(x)单调递增
∵a＋b＞c
∴f(c)＜f(a＋b)
∴c/(1＋c)＜(a＋b)/(1＋a＋b)＝a/(1＋a＋b)＋b/(1＋a＋b)＜a/(1＋a)＋b/(1＋b)