\(A=\frac{-9}{10^{2011}}+\frac{-9}{10^{2010}}\)
\(B=\frac{-9}{10^{2011}}+\frac{-19}{10^{2010}}\)
\(\frac{-9}{10^{2010}}>\frac{-19}{10^{2010}}\)
\(\Rightarrow\frac{-9}{10^{2011}}+\frac{-9}{10^{2010}}>\frac{-9}{10^{2011}}+\frac{-19}{10^{2010}}\)
\(\Rightarrow A>B\)