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若b>a>0,m>0,则a/b<(a+m)/(b+m)……(1)(高中代数课本第二册)本文将其进行一系列推广,目的在启发学生思维,使能举一反三,灵活应用。一、变形由不等式(1)可变形得 a/(a+m)m,还可变形得(a-m)/(b-m)(2n+1)~(1/2)/2。
If b>a>0 and m>0, then a/b<(a+m)/(b+m)...(1) (secondary textbook for high school algebra) This article will carry out a series of Inspiring students’ thinking, enabling them to use intuitions and flexible applications. First, the deformation by the inequality (1) can be transformed a / (a + m) m, but also can be modified (am)/(bm)(2n+1)~(1/2)/2.