作业帮计算x/(x^2-1) + (x^-x+1)/(x^3-x^2+x-1)+(x^2+x+1)/(x^3+x^2+x+1)
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/03 00:52:55
计算x/(x^2-1) + (x^-x+1)/(x^3-x^2+x-1)+(x^2+x+1)/(x^3+x^2+x+1)-2x^3/(x^4-1)
x/(x^2-1) + (x^2-x+1)/(x^3-x^2+x-1)+(x^2+x+1)/(x^3+x^2+x+1)-2x^3/(x^4-1)
=x/(x^2-1) -2x^3/(x^4-1) + (x^2-x+1)/(x^3-x^2+x-1)+(x^2+x+1)/(x^3+x^2+x+1)
=x*(x^2+1) /(x^4-1) -2x^3/(x^4-1)+ (x^2-x+1)/[(x-1)*(x^2 +1)]+ (x^2+x+1)/[(x+1)*(x^2+1)]
=(x^3-2x^3+x) / (x^4-1) + [(x^2-x+1)*(x+1)+ (x^2+x+1)*(x-1)] /[(x-1)*(x+1)*(x^2+1)]
=(-x^3+x) / (x^4-1) + 2x^3/(x^4 -1)
=(x^3+x) / (x^4-1)
=x*(x^2+1) / (x^4-1)
= x/(x^2-1)
=x/(x^2-1) -2x^3/(x^4-1) + (x^2-x+1)/(x^3-x^2+x-1)+(x^2+x+1)/(x^3+x^2+x+1)
=x*(x^2+1) /(x^4-1) -2x^3/(x^4-1)+ (x^2-x+1)/[(x-1)*(x^2 +1)]+ (x^2+x+1)/[(x+1)*(x^2+1)]
=(x^3-2x^3+x) / (x^4-1) + [(x^2-x+1)*(x+1)+ (x^2+x+1)*(x-1)] /[(x-1)*(x+1)*(x^2+1)]
=(-x^3+x) / (x^4-1) + 2x^3/(x^4 -1)
=(x^3+x) / (x^4-1)
=x*(x^2+1) / (x^4-1)
= x/(x^2-1)
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