\(B=\dfrac{-3}{31}+\dfrac{-6}{17}+\dfrac{1}{25}+\dfrac{-28}{31}+\dfrac{-11}{17}+\dfrac{-1}{5}\)
\(B=\left(\dfrac{-3}{31}+\dfrac{-28}{31}\right)+\left(\dfrac{-6}{17}+\dfrac{-11}{17}\right)+\left(\dfrac{-1}{5}+\dfrac{1}{25}\right)\)
\(B=\left(-1\right)+\left(-1\right)+\left(\dfrac{-4}{25}\right)\)
\(B=\left(-2\right)+\left(-\dfrac{4}{25}\right)\)
\(B=\dfrac{-54}{25}\)
\(C=\dfrac{-4}{12}+\dfrac{18}{45}+\dfrac{-21}{35}+\dfrac{6}{30}\)
\(C=\dfrac{-1}{3}+\dfrac{2}{5}+\dfrac{-2}{3}+\dfrac{-3}{5}+\dfrac{1}{5}\)
\(C=\left(\dfrac{-1}{3}+\dfrac{-2}{3}\right)+\left(\dfrac{2}{5}+\dfrac{-3}{5}+\dfrac{1}{5}\right)\)
\(C=-1+0\)
\(C=1\)
\(b,B=\left(\dfrac{-3}{31}+\dfrac{-28}{31}\right)+\left(\dfrac{-6}{17}+\dfrac{-11}{17}\right)+\left(\dfrac{1}{25}+\dfrac{-1}{5}\right)\\ B=-1+\left(-1\right)+\left(\dfrac{-1}{25}\right)\\ B=\left(-2\right)+\left(\dfrac{-1}{25}\right)\\ B=\dfrac{-50}{25}+\dfrac{-1}{25}=\dfrac{-51}{25}\)
\(b,B=\dfrac{-3}{31}+\dfrac{-6}{17}+\dfrac{1}{25}+\dfrac{-28}{31}+\dfrac{-11}{17}+\dfrac{-1}{5}\)
\(\Rightarrow B=\left(\dfrac{-3}{31}+\dfrac{-28}{31}\right)+\left(\dfrac{-6}{17}+\dfrac{-11}{17}\right)+\left(\dfrac{1}{25}+\dfrac{-1}{5}\right)\)
\(\Rightarrow B=\dfrac{-31}{31}+\dfrac{-17}{17}+\left(\dfrac{1}{25}+\dfrac{-5}{25}\right)\)
\(\Rightarrow B=\dfrac{-31}{31}+\dfrac{-17}{17}-\dfrac{4}{25}\)
\(\Rightarrow B=\left(-1\right)+\left(-1\right)-\dfrac{4}{25}\)
\(\Rightarrow B=\dfrac{-54}{25}\)
\(c,C=\dfrac{-4}{12}+\dfrac{18}{45}+\dfrac{-6}{9}+\dfrac{-21}{35}+\dfrac{6}{30}\)
\(\Rightarrow C=\dfrac{-1}{3}+\dfrac{2}{5}+\dfrac{-2}{3}+\dfrac{-3}{5}+\dfrac{1}{5}\)
\(\Rightarrow C=\left(\dfrac{-1}{3}+\dfrac{-2}{3}\right)+\left(\dfrac{2}{5}+\dfrac{-3}{5}+\dfrac{1}{5}\right)\)
\(\Rightarrow C=\dfrac{-3}{3}+\dfrac{0}{5}\)
\(\Rightarrow C=-1+0\\ \Rightarrow C=-1\)



