一道分式不等式：设文［1」、［Zj曾给出证明．本文将原不等式改进为再给出两种证法．先看三个引理：引理1设α1≥α2≥…≥αn＞0，0＜证明可参见［3」．引理2设αi、bi．证明可见[4]．引理3设αi、简证依引理2，并注意到幂平均不等注由题知，易得n—a＞0，而（此处由n（xf十 A fractional inequality: the text [1], [Zj has given proof. This article will improve the original inequality to give two kinds of evidence. Let us first look at three lemmas: Lemma 1 Let α1≥α2≥...≥αn>0,0< See the proof for [3]. Lemma 2 sets αi, bi. The proof is visible [4]. Lemma 3 assumes αi, the simple proof of Lemma 2, and notices that the power-average inequality is known by the inscription, which is easy to get n-a>0, and (here by n (xf ten