a-2b+(4b^2)/(a+2b)+(4a^2b)/(a^2-4b^2)

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