2005年湖南省数学竞赛压轴题为:若正数a,b,c满足b+a c=a+b c-ca+b,求证:a+b c≥174-1.这是从等式开始的解证多元分式不等式的问题,较新颖.考生的得分率很低,而且标准答案也不易,因而值得探讨其典型解证方法.证法1(标准答案)由条件有a+b c=ca+b+b+a c,令a+b=x,b+c=y,c+a=z,则a=x The 2005 Hunan Provincial Mathematics Competition Final Title: If the positive numbers a, b, c satisfy b+ac=a+b c-ca+b, verify that: a+bc≥174-1. This is the solution starting from the equation. The problem of multiple divisional inequalities is relatively new. The candidate’s score rate is very low, and the standard answer is not easy, so it is worth exploring its typical method of proof. The proof method 1 (standard answer) consists of conditions with a+bc=ca+b. +b+ac, let a+b=x, b+c=y,c+a=z, then a=x