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