若x+1/x=3,则x方/（x四次+x方+1）的值为
问题描述：
若x+1/x=3,则x方/（x四次+x方+1）的值为
答
(x^2)/(x^4+x^2+1)=1/[x^2+1/(x^2)+1],又因为：x+1/x=3，所以(x+1/x)^2=3^2=9,所以：x^2+1/(x^2)+2=9,所以：x^2+1/(x^2)+1=9-1=8，代入得：(x^2)/(x^4+x^2+1)=1/[x^2+1/(x^2)+1]=1/8
望君采纳，谢谢~
答
x+1/x=3
(x+1/x)²=3²
x²+1/x²+2*x*1/x=9
x²+1/x²+2=9
x²+1/x²=7
x方/（x四次+x方+1）
=1/（x四次/x²+x方/x²+1/x²）
=1/(x²+1+1/x²)
=1/(7+1)
=1/8