\(1001\left(\frac{2}{12012}+\frac{74}{555555}-\frac{2}{13.7.11.5}\right)=\frac{1001.2}{12012}+\frac{1001.74}{555555}-\frac{1001.2}{13.11.7.5}=\frac{1001.2}{12.1001}+\frac{1001.2.37}{1001.37.15}-\frac{1001.2}{1001.5}\)\(=\frac{1}{6}+\frac{2}{15}-\frac{2}{5}=\frac{5}{30}+\frac{4}{30}-\frac{12}{30}=-\frac{3}{30}=-\frac{1}{10}\)
\(1001\left(\frac{2}{12012}+\frac{74}{555555}-\frac{2}{13.7.77.5}\right)=\frac{1001.2}{12.1001}+\frac{1001.74}{555.1001}-\frac{1001.2}{85.1001}=\frac{1}{6}+\frac{74}{555}-\frac{2}{85}=11877\)