若x+1/x=5,求x^2/(x^4+x^2+1)的值

x+1/x=5
两边平方,其中中间一项=2*x*1/x=2
x^2+2+1/x^2=25
x^2+1/x^2=23

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

x+1/x=5解得：两边同时平方
x^2+1/x^2=25-2=23

x^2/(x^4+x^2+1)=1/x^2+1+x^2=24

解：(x+1/x)^2=25 得
x^2 + 1/x^2=23
x^2/(x^4+x^2+1)=1/(x^2 +1 + 1/x^2) (分子分母同时除以x^2)
=1/24