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因为x+1/x=√5
所以x²/(x⁴+x²+1)
=1/(x²+1+1/x²)
=1/(x²+2+1/x²-1)
=1/[(x²+2+1/x²)-1]
=1/[(x+1/x)²-1]
=1/[(√5)²-1]
=1/(5-1)
=1/4
所以x²/(x⁴+x²+1)
=1/(x²+1+1/x²)
=1/(x²+2+1/x²-1)
=1/[(x²+2+1/x²)-1]
=1/[(x+1/x)²-1]
=1/[(√5)²-1]
=1/(5-1)
=1/4
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