Question

解不等式:(3x2-14x+14)/(x2-6x+8)≥1

Answer 1

（3x^2-14x+14)/(x^2-6x+8)≥1
（3x^2-14x+14)/(x^2-6x+8)-1≥0
（3x^2-14x+14-x^2+6x-8)/(x^2-6x+8)≥0
(x^2-4x+3)/(x^2-6x+8)≥0
(x-1)(x-3)/(x-2)(x-4)≥0
得x≤1或2<x≤3或x>4

Answer 2

移项通分整理可得（x2-4x+3)/(x2-6x+8)≥0
将分式不等式化成整式不等式（x2-4x+3)(x2-6x+8)≥0且x2-6x+8不等0
即(x-1)(x-3)(x-2)(x-4)≥0且x2-6x+8不等0
利用数轴标根法可得愿不等式的解集{x|x<=1或2<x<=3或x>4}

Answer 3

x^2-6x+8＞0,

(x-4)(x-2)>0

所以x>4或x<2

x+3/x-1＞2.

x+3/x-3>0

(x^2-3x+3)/x>0

[(x-3/2)^2+3/4]/x>0

他的分子恒大于0

所以x>0

Answer 4

左边减右边得到：(2x^2-8x+6)/(x*2-6x+8)>=0即((x-1)(x-3)) / ((x-2)(x-4))>=0,得到x<=1或者2<x<=3或者x>4
故解集为{x|x<=1或2<x<=3或x>4}

Answer 5

（3x^2-14x+14)/(x^2-6x+8)≥1
移向：（3x^2-14x+14)/(x^2-6x+8)-1≥0
（3x^2-14x+14-x^2+6x-8)/(x^2-6x+8)≥0
(x^2-4x+3)/(x^2-6x+8)≥0
(x-1)(x-3)/(x-2)(x-4)≥0
得x≤1或2<x≤3或x>4
所以原不等式解集为{x|x≤1或2<x≤3或x>4}