化简[（x+1/x)^6-(x^6+1/x^6)-2]/[(x+1/x)^3+(x^3+1/x^3)]
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[（x+1/x)^6-(x^6+1/x^6)-2]/[(x+1/x)^3+(x^3+1/x^3)]
=[（x+1/x)^6-(x^6+1/x^6+2)]/[(x+1/x)^3+(x^3+1/x^3)]
=[（x+1/x)^6-(x^3+1/x^3)^2]/[(x+1/x)^3+(x^3+1/x^3)]
=[(x+1/x)^3+(x^3+1/x^3)][(x+1/x)^3-(x^3+1/x^3)]/[(x+1/x)^3+(x^3+1/x^3)]
=(x+1/x)^3-(x^3+1/x^3)
=(x^3+1/x^3+3x+3/x)-(x^3+1/x^3)
=3x+3/x.
=[（x+1/x)^6-(x^6+1/x^6+2)]/[(x+1/x)^3+(x^3+1/x^3)]
=[（x+1/x)^6-(x^3+1/x^3)^2]/[(x+1/x)^3+(x^3+1/x^3)]
=[(x+1/x)^3+(x^3+1/x^3)][(x+1/x)^3-(x^3+1/x^3)]/[(x+1/x)^3+(x^3+1/x^3)]
=(x+1/x)^3-(x^3+1/x^3)
=(x^3+1/x^3+3x+3/x)-(x^3+1/x^3)
=3x+3/x.
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