有一类分式不等式的证明在数学竞赛中经常出现,它的特点是不等式的一边各项形如 a2/(a±b)、a2/(b±c)、a/(a±b)或a/(b±c)的式子,通过构造向量并利用|a|·|b|≥|a·b|,可得到这类分式不等式的简捷证法,且构造向量的方法思路单一,操作简便,现举例说明． Proof of a class of fractional inequalities often occurs in mathematical competitions, which is characterized by the fact that each side of the inequality such as a2 / (a ​​± b), a2 / (b ± c), a / (a ​​± b) or a / (b ± c), we can get a simple and convenient method of constructing such a fractional inequality by constructing a vector and using | a | · | b | ≥ | a · b | Simple, is an example.