1) (a²+b²)/(ab)-2=(a²+b²-2ab)/(ab)=(a-b)²/(ab).
2) (2a²+2ab)/(a²+2ab+b²)-1=(2a²+2ab-a²-2ab-b²)/(a+b)²=(a²-b²)/(a+b)²
=(a-b)(a+b)/(a+b)²=(a-b)/(a+b).
3) (1/(a+b)+1/(a-b))=(a-b+a+b)=2a/((a+b)(a-b))=2a/(a²-b²).
4) ((a-b)²/ab)):((a-b)/(a+b))=(a-b)²*(a+b)/(ab*(a-b))=(a-b)*(a+b)/(ab)=(a²-b²)/(ab).
5) (2a/(a²-b²))*((a²-b²)/(ab))=2a*(a²-b²)/(ab*(a²-b²))=2/b.