Lời giải:
\(B=\frac{1}{11}.2\frac{30}{31}+3\frac{1}{55}.\frac{1}{31}-\frac{3}{11}+\frac{6}{55.31}\)
\(=\frac{1}{11}(2+\frac{30}{31})+(3+\frac{1}{55}).\frac{1}{31}-\frac{3}{11}+\frac{6}{55.31}\)
\(=\frac{2}{11}+\frac{30}{11.31}+\frac{3}{31}+\frac{1}{55.31}-\frac{3}{11}+\frac{6}{55.31}\)
\(=(\frac{2}{11}-\frac{3}{11})+\frac{31-1}{11.31}+\frac{3}{31}+(\frac{1}{55.31}-\frac{6}{55.31})\)
\(=\frac{-1}{11}+\frac{1}{11}-\frac{1}{11.31}+\frac{3}{31}-\frac{1}{11.31}\)
\(=\frac{-2}{11.31}+\frac{3}{31}=\frac{-2}{11.31}+\frac{33}{11.31}=\frac{33-2}{11.31}=\frac{31}{11.31}=\frac{1}{11}\)