(a²+b²/a²-b²-a-b/a+b)÷2ab/(a-b)(a+b)²
=[(a²+b²)/(a+b)-(a-b)/(a+b)] x(a-b)(a+b)²/2ab
=(a²+b²)(a+b)/2ab-(a-b)²(a+b)/2ab
=[(a²+b²)-(a-b)²](a+b)/2ab
=(a²+b²-a²+2ab-b²)(a+b)/2ab
=2ab(a+b)/2ab
=a+b