1. 2*a^(-1/3)/(2^(2/3)-3*a^(-1/3))=2*a^(-1/3)/(a^(-1/3)*(a^((2/3)-(-1/3))-3)=
=2*a^(-1/3)/(a^(-1/3)*(a^(3/3)-3))=2/(a-3).
2. a^(2/3)/(a^(5/3)-a^(2/3))=a^(2/3)/(a^(2/3)*(a^((5/3)-(2/3))-1)=
=a^(2/3)/(a^(2/3)*(a^(3/3)-1)=1/(a-1).
3. (a+1)/(a²-4a+3)=(a+1)/(a²-a-3a+3)=(a+1)/((a*(a-1)-3*(a-1))=
=(a+1)/((a-1)*(a-3)).
4. 2/(a-3)-1/(a-1)-(a+1)/((a-1)*(a-3))=2*(a-1)-(a-3)-(a+1)=2a-2-a+3-a-1=0.