Question

(2x+1)/(x-1)<=1的解集为？

解题过程，谢谢

Answer 1

解：(2x+1)/(x-1)≤1
[(2x+1)/(x-1)]-[(x-1)/(x-1)]≤0
(2x+1-x+1)/(x-1)≤0
等价转换，两个数的商是非正数，那么积也是非正数。
∴(x+2)(x-1)≤0
在数轴上表示（序轴标根法）解得
-2≤x≤1
∵x-1≠0
x≠1
∴这个不等式的解集为{x|-2≤x＜1}

Answer 2

因为x-1是分母，不等于0所以2x+1小于等于x-1 2x-x小于等于-1-1 x小于等于-2

Answer 3

(2x+1)/(x-1)<=1
(2x+1)/(x-1)-1<=0
(2x+1-x+1)/(x-1)<=0
(x+2)/(x-1)<=0
所以-2<=x<=1

Answer 4

(2x+1)/(x-1)-1<=0
(2x+1-x+1)/(x-1)<=0
(x+2)/(x-1)<=0
(x+2)(x-1)<=0且x-1不等于0
-2<=x<1

Answer 5

(2x+1)/(x-1)<=1
(2x+1)/(x-1)-1<=0
(2x+1-x+1)/(x-1)<=0
(x+2)(x-1)<=0
-2<=x<1