a: \(=\dfrac{-6\left(\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{31}\right)}{9\left(\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{31}\right)}=\dfrac{-6}{9}=\dfrac{-2}{3}\)
b: \(=\dfrac{\dfrac{1}{9}-\dfrac{1}{7}-\dfrac{1}{11}}{4\left(\dfrac{1}{9}-\dfrac{1}{7}-\dfrac{1}{11}\right)}+\dfrac{3\left(\dfrac{1}{5}-\dfrac{1}{25}-\dfrac{1}{125}-\dfrac{1}{625}\right)}{4\left(\dfrac{1}{5}-\dfrac{1}{25}-\dfrac{1}{125}-\dfrac{1}{625}\right)}\)
=1/4+3/4
=1
c: \(=\left[\dfrac{4-3}{386}\cdot\dfrac{193}{17}+\dfrac{33}{34}\right]:\left[\dfrac{14+11}{4002}\cdot\dfrac{2001}{25}+\dfrac{9}{2}\right]\)
\(=\left(\dfrac{1}{34}+\dfrac{33}{34}\right):\left(\dfrac{1}{2}+\dfrac{9}{2}\right)\)
=1/5
c) \(\left[\left(\dfrac{2}{193}-\dfrac{3}{386}\right)\cdot\dfrac{193}{17}+\dfrac{33}{34}\right]:\left[\left(\dfrac{7}{2001}+\dfrac{11}{4002}\right)\cdot\dfrac{2001}{25}+\dfrac{9}{2}\right]\)
\(=\left[\left(\dfrac{4}{386}-\dfrac{3}{386}\right)\cdot\dfrac{193}{17}+\dfrac{33}{34}\right]:\left[\left(\dfrac{14}{4002}+\dfrac{11}{4002}\right)\cdot\dfrac{2001}{25}+\dfrac{9}{2}\right]\)
\(=\left(\dfrac{1}{386}\cdot\dfrac{193}{17}+\dfrac{33}{34}\right):\left(\dfrac{25}{4002}\cdot\dfrac{2001}{25}+\dfrac{9}{2}\right)\)
\(=\left(\dfrac{193}{6562}+\dfrac{33}{34}\right):\left(\dfrac{2001}{4002}+\dfrac{9}{2}\right)\)
\(=\left(\dfrac{1}{34}+\dfrac{33}{34}\right):\left(\dfrac{1}{2}+\dfrac{9}{2}\right)\)
\(=\dfrac{34}{34}:\dfrac{10}{2}\)
\(=1:5=\dfrac{1}{5}\)
a) \(\dfrac{\dfrac{-6}{7}+\dfrac{6}{19}-\dfrac{6}{31}}{\dfrac{9}{7}-\dfrac{9}{19}+\dfrac{9}{31}}\)
\(=\dfrac{-6\left(\dfrac{1}{7}-\dfrac{1}{19}+\dfrac{1}{31}\right)}{9\left(\dfrac{1}{7}-\dfrac{1}{19}+\dfrac{1}{31}\right)}\)
\(=\dfrac{-6}{9}\)
\(=-\dfrac{2}{3}\)
b) \(\dfrac{\dfrac{1}{9}-\dfrac{1}{7}-\dfrac{1}{11}}{\dfrac{4}{9}-\dfrac{4}{7}-\dfrac{4}{11}}+\dfrac{\dfrac{3}{5}-\dfrac{3}{25}-\dfrac{3}{125}-\dfrac{3}{625}}{\dfrac{4}{5}-\dfrac{4}{25}-\dfrac{4}{125}-\dfrac{4}{625}}\)
\(=\dfrac{\dfrac{1}{9}-\dfrac{1}{7}-\dfrac{1}{11}}{4\left(\dfrac{1}{9}-\dfrac{1}{7}-\dfrac{1}{11}\right)}+\dfrac{3\left(\dfrac{1}{5}-\dfrac{1}{25}-\dfrac{1}{125}-\dfrac{1}{625}\right)}{4\left(\dfrac{1}{5}-\dfrac{1}{25}-\dfrac{1}{125}-\dfrac{1}{625}\right)}\)
\(=\dfrac{1}{4}+\dfrac{3}{4}\)
\(=\dfrac{4}{4}=1\)
