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