\(\left(\frac{1999}{2011}-\frac{2001}{1999}\right)-\left(\frac{-12}{1999}-\frac{12}{2001}\right)=\frac{1999}{2011}-\frac{2011}{1999}+\frac{12}{1999}+\frac{12}{2001}\)
\(=\left(\frac{1999}{2011}+\frac{12}{2011}\right)+\left(\frac{-2011}{1999}+\frac{12}{1999}\right)=\frac{2011}{2011}+\left(\frac{-2011}{2011}\right)=1+\left(-1\right)=0\)