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x/x^2+x+1=-1/22x^2/(x^2-x+1)+x-1/x^3-1
题目详情
x/x^2+x+1=-1/22x^2/(x^2-x+1)+x-1/x^3-1
▼优质解答
答案和解析
x/(x^2+x+1)=-1/2
x^2+x+1=-2x
则x^2-x+1=-4x
且x^2+1=-3x
2x^2/(x^2-x+1)+(x-1)/(x^3-1)
=2x^2/(x^2-x+1)+(x-1)/(x-1)(x^2+x+1)
=2x^2/(x^2-x+1)+1/(x^2+x+1)
=2x^2/(-4x)+1/(-2x)
=-x/2-1/2x
=-(x^2+1)/2x
=-(-3x)/2x
=3/2
x^2+x+1=-2x
则x^2-x+1=-4x
且x^2+1=-3x
2x^2/(x^2-x+1)+(x-1)/(x^3-1)
=2x^2/(x^2-x+1)+(x-1)/(x-1)(x^2+x+1)
=2x^2/(x^2-x+1)+1/(x^2+x+1)
=2x^2/(-4x)+1/(-2x)
=-x/2-1/2x
=-(x^2+1)/2x
=-(-3x)/2x
=3/2
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