计算1/1-x + 1/1+x + 4/1+x的四次方 + 2/x²+1

1/(1-x)+1/(1+x)+4/(1+x^4)+2/(x²+1)
= 1/(1-x)+1/(1+x)+2/(1+x²)+4/(1+x^4)
= [(1+x)+(1-x)]/[(1-x)(1+x)]+2/(1+x²)+4/(1+x^4)
= 2/(1-x²)+2/(1+x²)+4/(1+x^4)
= 2[(1+x²)+(1-x²)]/[(1-x²)(1+x²)]+4/(1+x^4)
= 4/(1-x^4)+4/(1+x^4)
= 4[(1+x^4)+(1-x^4)]/[(1-x^4)(1+x^4)]
= 8/(1-x^8)