Question

不等式1/(x-1)≥1/(x²-1)的解集是

Answer 1

1/(x-1)-1/(x+1)(x-1)>=0
(x+1-1)/(x+1)(x-1)>=0
x/(x+1)(x-1)>=0
即x(x+1)(x-1)>=0
零点是-1,0,1
分母不等于0
所以-1<x≤0,x>1

Answer 2

1/(x-1)≥1/(x²-1) (x+1)/(x²-1)-1/(x²-1)≥0
(x+1-1)/(x²-1)≥0 x/(x²-1)≥0
x(x²-1)≥0 且(x²-1)≠0 x(x+1)(x-1)≥0且(x²-1)≠0

不等式1/(x-1)≥1/(x²-1)的解集是 {x|-1<x≤0 或 x>1}