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