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