| 1/(x+1) |

来源：学生作业帮助网编辑：作业帮时间：2024/11/17 07:47:34

| 1/(x+1) |
| 1/(x+1) |

| 1/(x+1) |
左右同乘|x+1|
1

上式等价于|x+1|>=1。即：x+1>=1或x+1<=-1。所以x>=0或x<=-2

-1<1/(x+1)<1
X>0 或 x<-2

-1≤1/(x+1)≤1
1/(x+1)+1≥0 1/(x+1)-1≤0
(x+2)/(x+1)≥0 x/(x+1)≥0
x≤-2 OR x>-1 x≥0 OR x<-1
x≤-2 OR x≥0

两边平方得：｛1/（x＋1）｝≤1,①1/x＋1≤1.②1/x＋1≥－1.当①时，同时减去1，得1/(x＋1)－1≤0,即1/(x＋1)－(x＋1)/(x＋1)≤0,整理得－x/(x＋1)≤0，即－x(x＋1)≤0，解得x≤0或x≥1，当②时同理

这是一道比较典型的绝对值不等式与倒数不等式相结合的题目
由题设条件
去绝对值符号可以得到
-1<=1/(x+1)<= 1
再由倒数关系
则x+1>=1或
x+1<-1
即x>=0或x<=-2 是所求不等式的最终解

| 1/(x+1) | ≤ 1
-1≤ 1/(x+1) ≤ 1且x+1≠0 x≠-1
-1＜ 1/(x+1) ≤ 1
将两个不等式分开化简，同时乘以x+1,得
1≤x+1 x≥0
x<-2
所以x≥0 或x<-2

1/(x+1) <=1或1/(x+1) >=-1 x<=-2或x>=0

猪啊你

解:|1/(x+1)|<=1→1<=|x+1|→1<=x+1或x+1<=-1→0<=x 或x<=-2

所以x+1小于等于1，所以x小于等于0

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