(a+m)/(b+m)-a/b=(a+m)b/[(b+m)b]-(b+m)a/[(b+m)b]=(ab+bm)/(b²+bm)-(ab+am)/(b²+bm)=[2ab+(b-a)m]/(b²+bm)∵a0,b>0∴[2ab+(b-a)m]/(b²+bm)>0∴(a+m)/(b+m)>a/b