1/a-b-1/a+b-2b/a^2+b^2-4b^3/a^4+b^4+8b^7/b^2-a^2

1/a-b-1/a+b-2b/a^2+b^2-4b^3/a^4+b^4+8b^7/b^2-a^2
1/a-b-1/a+b-2b/a^2+b^2-4b^3/a^4+b^4+8b^7/b^2-a^2

1/a-b-1/a+b-2b/a^2+b^2-4b^3/a^4+b^4+8b^7/b^2-a^2
1/(a-b)-1/(a+b)-2b/(a^2+b^2)-4b^3/(a^4+b^4)+8b^7/(b^2-a^2)
=(a+b)/(a^2-b^2)-(a-b)/(a^2-b^2)-8b^7/(a^2-b^2)-2b/(a^2+b^2)-4b^3/(a^4+b^4)
=2b(1-b^6)/(a^2-b^2)-2b/(a^2+b^2)-4b^3/(a^4+b^4)
=2b[(1-b^6)(a^2+b^2)-(a^2-b^2)]/(a^4-b^4)-4b^3/(a^4+b^4)
=2b^3(2-a^2-b^2)/(a^4-b^4)-4b^3/(a^4+b^4)
=2b^3[(2-a^2-b^2)(a^4+b^4)-2(a^4-b^4)]/(a^8-b^8)
=2b^3[4b^4-(a^4+b^4)(a^2+b^2)]/(a^8-b^8).