分解下列因式

解：1. [4/(x^2-y^2)+(x+y)/(x^2y-y^2x)]/[(x^2+xy-2y^2)/(x^2y+2xy^2)]，可以把这个因式分步化简，4/(x^2-y^2)+(x+y)/(x^2y-y^2x)=4/(x+y)(x-y)-(x+y)/xy(x-y)=[4xy-(x+y)^2]/(x+y)(x-y)xy=-(x-y)^2/(x+y)(x-y)xy=-(x-y)/(x+y)xy。 (x^2+xy-2y^2)/(x^2y+2xy^2)=(x-y)(x+2y)/(x+2y)xy=(x-y)/xy。 所以[4/(x^2-y^2)+(x+y)/(x^2y-y^2x)]/[(x^2+xy-2y^2)/(x^2y+2xy^2)]=[-(x-y)/(x+y)xy]/[(x-y)/xy]=-1/(x+y)。

2. [(1/a+b)^2-1/(a-b)^2]/(1/a+b-1/a-b)=[(1/a+b)+(1/a-b)][(1/a+b)+(1/a-b)]/(1/a+b-1/a-b)=(1/a+b)+(1/a-b)=2a/(a+b)(a-b)。