请问x2-3x+1/x2-1≥1详细解法x后是平方,

来源:学生作业帮助网 编辑:作业帮 时间:2024/03/29 16:55:26
请问x2-3x+1/x2-1≥1详细解法x后是平方,

请问x2-3x+1/x2-1≥1详细解法x后是平方,
请问x2-3x+1/x2-1≥1详细解法
x后是平方,

请问x2-3x+1/x2-1≥1详细解法x后是平方,
(x²-3x+1)/(x²-1)-1>=0
(x²-3x+1-x²+1)/(x²-1)>=0
(-3x+2)/(x+1)(x-1)>=0
(3x-2)(x+1)(x-1)

(x²-3x+1)/(x²-1)-1>=0
(x²-3x+1-x²+1)/(x²-1)>=0
(-3x+2)/(x+1)(x-1)>=0 等价于
(3x-2)(x+1)(x-1)<=0 且X不等于1和-1
余下用数轴法解答
得 x<-1,2/3≤x<1

(x²-3x+1)/(x²-1)-1>=0
(x²-3x+1-x²+1)/(x²-1)>=0
(-3x+2)/(x+1)(x-1)>=0
(3x-2)(x+1)(x-1)<=0
分母不等于0,x不等于1,-1,但可以等于2/3
所以x<-1,2/3≤x<1