如果x+1／x=3,则x²／﹙x⁴+x²+1﹚=﹙﹚

题目

如果x+1／x=3,则x²／﹙x⁴+x²+1﹚=﹙﹚
填空,

答案

x+1/x=3
两边平方得
x²+2+1/x²=9
x²+1/x²=7
x²/(x^4+x^2+1)
=1/(x²+1+1/x²)
=1/[(x²+1/x²)+1]
=1/(7+1)
=1/8