数学题帮忙解一下……
计算，请写明详细步骤
(x^3-1)÷(x^3+2x^2+2x+1)+(x^3+1)÷(x^3-2x^2+2x-1)-2(x^2+1)÷(x^2-1)
参考答案:x^3+2x^2+2x+1=x^2(x+1)+x(x+1)+x+1
=(x^2+x+1)(x+1)
同理x^3-2x^2+2x-1=x^2(x-1)-x(x-1)+x-1
=(x^2-x+1)(x-1)
(x^3-1)÷(x^3+2x^2+2x+1)+(x^3+1)÷(x^3-2x^2+2x-1)
=(x-1)(x^2+x+1)÷(x^3+2x^2+2x+1)+(x+1)(x^2-x+1)÷(x^3-2x^2-2x+1)
=(x-1)/(x+1)+(x+1)/(x-1)
=2(x^2+1)/(x^2-1)
2(x^2+1)/(x^2-1)-2(x^2+1)÷(x^2-1)
=0