\(A=\frac{2009\cdot2010-2}{2008+2008\cdot2010}=\frac{\left(2008+1\right)\cdot2010-2}{2008+2008\cdot2010}=\frac{\left(2008\cdot2010\right)+\left(2010-2\right)}{2008+2008\cdot2010}=\frac{2008\cdot2010+2008}{2008+2008\cdot2010}=1\)\(B=\frac{-2009\cdot20102010}{20092009\cdot2010}=\frac{-2009\cdot2010\cdot10001}{2009\cdot10001\cdot2010}=-1\)
=>A+B=1+(-1)=0
Vậy A+B=0
\(A=\frac{2009.2010-2}{2008+2008.2010}=\frac{2008.2010+2010-2}{2008+2008.2010}=\frac{2008.2010+2008}{2008+2008.2010}=1\)
\(B=\frac{-2009.20102010}{20092009.2010}=\frac{-2009.2010.10001}{2009.10001.2010}=-1\)
Vậy \(a+b=1+\left(-1\right)=0\)
