若x/x^2-3x+1=2,求分式x^2/x^4+x^2+1的值

若x/x^2-3x+1=2,求分式x^2/x^4+x^2+1的值
若x/x^2-3x+1=2,求分式x^2/x^4+x^2+1的值

若x/x^2-3x+1=2,求分式x^2/x^4+x^2+1的值
x/(x²-3x+1)=2
得 1/(x-3+1/x)=2
x-3+1/x=1/2
x+1/x=7/2
x²/x^4+x²+1=1/(x²+1+1/x²)
=1/[(x+1/x)²-1]
=1/(49/4-1)
=4/45