化简a-b/a+2b÷a^2-b^2/a^2+4ab+4b^2-1

原式=[(a-b)/(a+2b)]×[(a+2b)^2/(a+b)(a-b)]-1 =(a+2b)/(a+b)-1 =(a+2b-a-b)/(a+b) =b/(a+b)