题目

问一道数学题 当x>2时,试比较分式(x-2)/(x-1)和(x-3)/(x-2)的值的大小

提问时间：2021-03-24

答案

(x-2)/(x-1)
=(x-1-1)/(x-1)
=(x-1)/(x-1)-1/(x-1)
=1-1/(x-1)
(x-3)/(x-2)
=(x-2-1)/(x-2)
=(x-2)/(x-2)-1/(x-2)
=1-1/(x-2)
x>2
所以x-1>x-2>0
所以1/(x-1)-1/(x-2)
-1/(x-1)>1-1/(x-2)
所以(x-2)/(x-1)>(x-3)/(x-2)