已知x+1/x=4,则（x^2）/[(x^4)+(x^2)+1]的值为多少?帮个忙!

题目

已知x+1/x=4,则（x^2）/[(x^4)+(x^2)+1]的值为多少?帮个忙!

答案

x+1/x=4
两边平方得
x²+2+1/x²=16
x²+1/x²=14
x²/(x^4+x^2+1)
=1/(x²+1+1/x²)
=1/[(x²+1/x²)+1]
=1/(14+1)
=1/15