Question

求解一道分式不等式.1-x^2/(x^2+1)^2>0和1-x^2/(x^2+1)^2

Answer 1

1.1-x^2/(x^2+1)^2>0

1-[x/(x^2+1)]^2>0

{1+[x/(x^2+1)]}*{1-[x/(x^2+1)]}>0

[(x^2+x+1)/(x^2+1)]*[(x^2-x+1)/(x^2+1)]>0很成立

x取一切实数

2.与之相反,x无解

1.（1-x^2)/(x^2+1)^2>0

(x^2+1)^2>0恒成立

所以（1-x^2)>0

x^21或者x