众所周知,对于任意的正实数a,有a+1/a≥2 ①其中当且仅当a=1时等号成立. 事实上,①可变为 a-1≥1-(1/a) ②即任一正实数与1的差不小于1与它的倒数的差. 下面应用②来证明一类与分式有关的不等式,可见这一基本结论的变形具有十分重要的应用价值. It is known that for any positive real number a, there is a+1/a≥2 1 where the equal sign holds if and only if a = 1. In fact, 1 can be changed to a-1≥1-(1/a) 2 That is, the difference between any positive real number and 1 is not less than the difference between 1 and its reciprocal. Applying the following 2 to prove a class of fractional inequality, it can be seen that the deformation of this basic conclusion has very important application value.