\(A=\frac{3b\left(2a-1\right)+6a-3}{2a+2ab-b-1}=\frac{6ab-3b+6a-3}{2a+2ab-b-1}=\frac{6ab+6a-3b-3}{2a+2ab-b-1}\)
\(=\frac{6a\left(b+1\right)-3\left(b+1\right)}{2a\left(b+1\right)-\left(b+1\right)}=\frac{\left(b+1\right)\left(6a-3\right)}{\left(b+1\right)\left(2a-1\right)}=\frac{6a-3}{2a-1}=\frac{3a-3}{-1}\)
\(=\frac{3\left(a-1\right)+2012}{-1}=\frac{3a-3+2012}{-1}=-\frac{3a-2009}{1}=\frac{3a+2009}{1}\)
\(\Rightarrow A=\frac{3a+2009}{1}\)