若1/x+x=-5，则x^2/(x^4+x^2+1)=_______.

x^2/(x^4+x^2+1)=1/(x^2+1+1/x^2)
=1/[(x+1/x)^2-2+1]=1/24

1/x+x=-5
两边平方
x^2+2x*1/x+1/x^2=25
x^2+2+1/x^2=25
x^2+1/x^2=23

x^2/(x^4+x^2+1)
上下除以x^2
=1/(x^2+1+1/x^2)
=1/(1+23)
=1/24

上下同除x^2，分子为1，分母可化为(x+1/x)^2-1，所以分母值为24
所以结果为1/24