{(a-b)/(a+2b)}/{(a²-b²)/(a²+4ab+4b²)}-1
={(a-b)/(a+2b)}/{(a+b)(a-b)/(a+2b)²}-1
=(a-b)(a+2b)²/(a+b)(a-b)(a+2b)²-1
=(a+2b)/(a+b)-1
=b/(a+b)
{(a-b)/(a+2b)}/{(a²-b²)/(a²+4ab+4b²)}-1
={(a-b)/(a+2b)}/{(a+b)(a-b)/(a+2b)²}-1
=(a-b)(a+2b)²/(a+b)(a-b)(a+2b)²-1
=(a+2b)/(a+b)-1
=b/(a+b)