如果X+1/X=3,求X^2/(X^4+X^2+1)的值

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如果X+1/X=3,求X^2/(X^4+X^2+1)的值

如果X+1/X=3,求X^2/(X^4+X^2+1)的值
如果X+1/X=3,求X^2/(X^4+X^2+1)的值

如果X+1/X=3,求X^2/(X^4+X^2+1)的值
x²/(x⁴+x²+1)
=1/(x²+1+1/x²)
=1/(x²+1/x²+2-1)
=1/[(x+1/x)²-1]
=1/(3²-1)
=1/8