\(B=\dfrac{13\cdot4^6\left(28\dfrac{7}{13}-27\dfrac{5}{18}\right)}{59\cdot2^{12}\left(\dfrac{5}{14}+\dfrac{5}{84}+\dfrac{5}{204}+\dfrac{5}{374}\right)}\)
\(=\dfrac{13}{59}\cdot\dfrac{2^{12}}{2^{12}}\cdot\dfrac{28+\dfrac{7}{13}-27-\dfrac{5}{18}}{5\left(\dfrac{1}{14}+\dfrac{1}{84}+\dfrac{1}{204}+\dfrac{1}{374}\right)}\)
\(=\dfrac{13}{59}\cdot\dfrac{1+\dfrac{7}{13}-\dfrac{5}{18}}{5\left(\dfrac{1}{2\cdot7}+\dfrac{1}{7\cdot12}+\dfrac{1}{12\cdot17}+\dfrac{1}{17\cdot22}\right)}\)
\(=\dfrac{13}{59}\cdot\dfrac{1+\dfrac{7}{13}-\dfrac{5}{18}}{\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{22}}\)
\(=\dfrac{13}{59}\cdot\dfrac{\dfrac{295}{234}}{\dfrac{1}{2}-\dfrac{1}{22}}=\dfrac{13}{59}\cdot\dfrac{295}{234}:\dfrac{10}{22}\)
\(=13\cdot\dfrac{5}{234}\cdot\dfrac{22}{10}\)
\(=\dfrac{5}{18}\cdot\dfrac{11}{5}=\dfrac{11}{18}\)
