[1/(a-b) - 1/(a+b）] ÷2b/(a²-2ab+b²)
=[(a+b)-(a-b)]/[(a+b)(a-b)] × (a-b)²/(2b)
=(2b)/(a+b) × (a-b)/(2b)
=(a-b)/(a+b)
.
m/(m-n) - n/(m+n) + 2mn/(m²-n²)
=[m(m+n)-n(m-n)+2mn)]/[(m+n)(m-n)]
=(m²+mn-mn+n²+2mn)/[(m+n)(m-n)]
=(m+n)²/[(m+n)(m-n)]
=(m+n)/(m-n)