Question

解下列不等式（3）2/x-1+1≥x（4）3/x-1＜4/x+1-1

Answer 1

（3）2/(x-1)+1≥x
2/(x-1)-(x-1)≥0
(2-x²+2x-1)/(x-1)≥0
(x²-2x-1)/(x-1)≤0
解 x²-2x-1=0得x=1-√2，x=1+√2
所以原不等式的解是x≤1-√2，1<x≤1+√2

（4）3/(x-1)＜4/(x+1)-1
3/(x-1)-4/(x+1)+1＜0
(3x+3-4x+4+x²-1)/[(x-1)(x+1)]<0
(x²-x+6)/[(x-1)(x+1)]<0
(x+2)(x-3)/[(x-1)(x+1)]<0
所以原不等式的解是-2<x<-1，1<x<3

Answer 2

(x-1)/2 +1≥x 得1/2≥x/2 所以x小于等于1

3/x-1＜4/x+1-1
两边同时乘以12得到
4X-4＜3x+3-12 4x-3x＜3-12+4 x＜-5

Answer 3

(3)2/X-1≥X-1 X-1≥2X-2 X-2X≥-2+1 -X≥-1 X≥1
(4)4X-4＜3x+3-12 4x-3x＜3-12+4 x＜-5

Answer 4

去分母,同时乘x