∵x+1/x=3
∴(x+1/x)²=9
即x²+1/x²+2=9
x²+1/x²=7
x²/(x^4+x²+1)
=x²/(x²(x²+1+1/x²))
=1/(x²+1/x²+1)
=1/(7+1)
=1/8