构造法是一种创造性的解题方法,它是根据数学问题的题设和结论特征,构造出新的易解决的问题,从而得到简捷、明快、新颖的解法。本文笔者以高二数学教材上册中的一道例题为例说明构造法证不等式的几种策略。题目已知a,b,m∈R~+,且a＜b,求证：(a+m)/(b+m)＞a/b。一、构造函数,利用其单调性分析不等式左边为(a+m)/(b+m),而右边可写成(a+0)/(b+0),从而构造函数f(x)=(a+x)/(b+x),研究其单调性可获问题的解决。证法1 构造函数 The construction method is a creative problem-solving method. It is based on the problem of mathematics questions and the characteristics of conclusions to construct a new easy-to-solve problem, so as to obtain a simple, clear, and novel solution. In this paper, the author uses the example of an example in the second grade mathematics textbook as an example to illustrate several strategies for constructing forensic inequality. The subject is known as a, b, m∈R~+, and aa/b. First, the constructor, using its monotonicity analysis inequality, the left side is (a+m)/(b+m), and the right side can be written as (a+0)/(b+0), thus the constructor f(x)=( a+x)/(b+x) to study the solution to the problem of monotony. Proof 1 constructor