数学高手请进!
(X*X+2X-2)/(3+2X-X*X)<X
怎么化简?
参考答案:解:(X2+2X-2)/(3+2X-X2)<X
(x2+2x-2)/(3+2x-x2)-(3x+2x2-x3)/(3+2x-x2)<0
(x3-x2-x-2)/(3+2x-x2)<0
(x-2)(x2+x+1)/(x2-2x-3)>0
∵ x2+x+1恒大于0
∴原不等式化为(x-2)(x-3)(x+1)>0
原不等式的解集为-1<x<2或x>3
(X*X+2X-2)/(3+2X-X*X)<X
怎么化简?
参考答案:解:(X2+2X-2)/(3+2X-X2)<X
(x2+2x-2)/(3+2x-x2)-(3x+2x2-x3)/(3+2x-x2)<0
(x3-x2-x-2)/(3+2x-x2)<0
(x-2)(x2+x+1)/(x2-2x-3)>0
∵ x2+x+1恒大于0
∴原不等式化为(x-2)(x-3)(x+1)>0
原不等式的解集为-1<x<2或x>3