设x＞1,比较x/﹙x-1﹚与﹙x+1﹚/x的大小

Question

设x＞1,比较x/﹙x-1﹚与﹙x+1﹚/x的大小

Answer 1

x/﹙x-1）-﹙x+1﹚/x=（x²-x-x²+1）/（x²-x）=（1-x）/（x²-x）=-1/x小于0,故x/﹙x-1）＜﹙x+1﹚