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化简[（X+1/X)^6-（X^6+1/X^6)-2]/[(X+1/X)^3+(X^3+1/X^3)]
题目详情
化简[（X+1/X)^6-（X^6+1/X^6)-2]/[(X+1/X)^3+(X^3+1/X^3)]
▼优质解答
答案和解析
[（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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