1/(a-b)+1/(a+b)+2a/(a^2+b^2)+4a^3/(a^4+b^4)=2a/(a^2-b^2)+2a/(a^2+b^2)+4a^3/(a^4+b^4)=4a^3/(a^4-b^4)+4a^3/(a^4+b^4)=4a^3[(a^4+b^4)+(a^4-b^4)]/(a^8-b^8)=4a^7/(a^8-b^8)