1. (a(a-2b)+2b(a-2b)+4b^2)/(a-2b)=(a^2-2ab+2ab-4b^2+4b^2)/(a-2b)=a^2/(a-2b);
2. (a(a+2b)-2ab)/(a+2b)=(a^2+2ab-2ab)/(a+2b)=a^2/(a+2b);
3. (a^2/(a-2b))/(a^2/(a+2b))=(a^2/(a-2b))*((a+2b)/a^2)=(a+2b)/(a-2b);
4. (a+2b)/(a-2b) + 1=(a+2b+a-2b)/(a-2b)=2a/(a-2b).