问题: 分式化简，急得很！！
x/(x^3+x^2y+xy^2+y^3)+y/(x^3-x^2y+xy^2-y^3)+
1/(x^2-y^2)-1/(x^2+y^2)-(x^2+3y^2)/(x^4+y^4)
解答:
x/(x³+x²y+xy²+y³) + y/(x³-x²y+xy²-y³) +
+ 1/(x²-y²) - 1/(x²+y²) - (x²+3y²)/(x^4+y^4)
= x/[(x+y)(x²+y²)] + y/[(x-y)(x²+y²)] +
+ 1/(x²-y²) - 1/(x²+y²) - (x²+3y²)/(x^4+y^4)
= [x(x-y)+y(x+y)]/[(x²-y²)(x²+y²)] +
+ 1/(x²-y²) - 1/(x²+y²) - (x²+3y²)/(x^4+y^4)
= [x²+y²]/[(x²-y²)(x²+y²)] + 1/(x²-y²) -
- 1/(x²+y²) - (x²+3y²)/(x^4+y^4)
= 2/(x²-y²) - 1/(x²+y²)-(x²+3y²)/(x^4+y^4)
= [2(x²+y²)-(x²-y²)]/[(x²-y²)(x²+y²)] - (x²+3y²)/(x^4+y^4)
= (x²+3y²)/(x^4-y^4) - (x²+3y²)/(x^4+y^4)
= 2y^4•(x²+3y²)/(x^8-y^8)
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