a) \(\frac{\left(\right. x + \frac{3}{4} \left.\right) . \frac{7}{2} - \frac{1}{6}}{- \left(\right. \frac{4}{5} + \frac{1}{3} \left.\right) . \frac{1}{2} + 1} = 2 \frac{33}{52}\)

\(\Leftrightarrow \frac{\left(\right. x + \frac{3}{4} \left.\right) . \frac{7}{2} - \frac{1}{6}}{- \frac{17}{15} . \frac{1}{2} + 1} = \frac{137}{52}\)

\(\Leftrightarrow \frac{\left(\right. x + \frac{3}{4} \left.\right) . \frac{7}{2} - \frac{1}{6}}{\frac{13}{30}} = \frac{137}{52}\)

\(\Leftrightarrow \left(\right. x + \frac{3}{4} \left.\right) . \frac{7}{2} - \frac{1}{6} = \frac{137}{52} . \frac{13}{30}\)

\(\Leftrightarrow \left(\right. x + \frac{3}{4} \left.\right) . \frac{7}{2} - \frac{1}{6} = \frac{137}{120}\)

\(\Leftrightarrow \left(\right. x + \frac{3}{4} \left.\right) . \frac{7}{2} = \frac{137}{120} + \frac{1}{6}\)

\(\Leftrightarrow \left(\right. x + \frac{3}{4} \left.\right) . \frac{7}{2} = \frac{157}{120}\)

\(\Leftrightarrow x + \frac{3}{4} = \frac{157}{120} : \frac{7}{2}\)

\(\Leftrightarrow x + \frac{3}{4} = \frac{157}{420}\)

\(\Leftrightarrow x = \frac{157}{420} - \frac{3}{4}\)

\(\Leftrightarrow x = - \frac{79}{210}\)

Vậy \(x = - \frac{79}{210}\).

b) \(\frac{\left(\right. 5 - \frac{2}{7} \left.\right) . \frac{7}{9} . \frac{3}{5}}{\left(\right. 3 x - \frac{5}{6} \left.\right) : \frac{1}{7}} = 5 \frac{5}{21}\)

\(\Leftrightarrow \frac{\left(\right. 5 - \frac{2}{7} \left.\right) . \frac{7}{15}}{\left(\right. 3 x - \frac{5}{6} \left.\right) : \frac{1}{7}} = \frac{110}{21}\)

\(\Leftrightarrow \frac{\frac{33}{7} . \frac{7}{15}}{\left(\right. 3 x - \frac{5}{6} \left.\right) : \frac{1}{7}} = \frac{110}{21}\)

\(\Leftrightarrow \frac{\frac{11}{5}}{\left(\right. 3 x - \frac{5}{6} \left.\right) : \frac{1}{7}} = \frac{110}{21}\)

\(\Leftrightarrow \left(\right. 3 x - \frac{5}{6} \left.\right) : \frac{1}{7} = \frac{11}{5} : \frac{110}{21}\)

\(\Leftrightarrow \left(\right. 3 x - \frac{5}{6} \left.\right) : \frac{1}{7} = \frac{21}{50}\)

\(\Leftrightarrow 3 x - \frac{5}{6} = \frac{21}{50} . \frac{1}{7}\)

\(\Leftrightarrow 3 x - \frac{5}{6} = \frac{3}{50}\)

\(\Leftrightarrow 3 x = \frac{3}{50} + \frac{5}{6}\)

\(\Leftrightarrow 3 x = \frac{67}{75}\)

\(\Leftrightarrow x = \frac{67}{75} : 3\)

\(\Leftrightarrow x = \frac{67}{225}\)

Vậy \(x = \frac{67}{225}\).

) \(A = \frac{3}{5} . \frac{6}{7} + \frac{3}{7} . \frac{3}{5} - \frac{2}{7} . \frac{3}{5}\)

    \(A = \frac{3}{5} . \frac{6}{7} + \frac{3}{5} . \frac{3}{7} - \frac{2}{7} . \frac{3}{5}\)

    \(A = \frac{3}{5} . \left(\right. \frac{6}{7} + \frac{3}{7} - \frac{2}{7} \left.\right)\)

    \(A = \frac{3}{5} . 1\)

    \(A = \frac{3}{5}\)

b) \(B = \left(\right. - 13. \frac{2}{5} + \frac{- 2}{9} : 2 \frac{1}{2} + \frac{2}{5} . \frac{11}{9} \left.\right) . 2 \frac{1}{2}\)

    \(B = \left(\right. - 13. \frac{2}{5} + \frac{- 2}{9} : \frac{5}{2} + \frac{2}{5} . \frac{11}{9} \left.\right) . \frac{5}{2}\)

    \(B = \left(\right. - 13. \frac{2}{5} + \frac{- 2}{9} . \frac{5}{2} + \frac{2}{5} . \frac{11}{9} \left.\right) . \frac{5}{2}\)

    \(B = \left(\right. - 13 + \frac{- 2}{9} + \frac{11}{9} \left.\right) . \frac{2}{5} . \frac{5}{2}\)

    \(B = - 13 + \left(\right. \frac{- 2}{9} + \frac{11}{9} \left.\right)\)

    \(B = - 13 + 1\)

    \(B = - 12\)

c) \(C = \left(\right. \frac{- 4}{5} + \frac{5}{7} \left.\right) : \frac{2}{3} + \left(\right. \frac{- 1}{5} - \frac{2}{7} \left.\right) : \frac{2}{3}\)

    \(C = \left(\right. \frac{- 4}{5} + \frac{5}{7} \left.\right) . \frac{3}{2} + \left(\right. \frac{- 1}{5} - \frac{2}{7} \left.\right) . \frac{3}{2}\)

    \(C = \left(\right. \frac{- 4}{5} + \frac{5}{7} + \frac{- 1}{5} - \frac{2}{7} \left.\right) . \frac{3}{2}\)

    \(C = \left(\right. \frac{- 4}{5} + \frac{- 1}{5} + \frac{5}{7} + \frac{2}{7} \left.\right) . \frac{3}{2}\)

    \(C = \left(\right. - 1 + 1 \left.\right) . \frac{3}{2}\)

    \(C = 0\)

    d) \(D = \frac{4}{9} : \left(\right. \frac{1}{15} - \frac{2}{3} \left.\right) + \frac{4}{9} : \left(\right. \frac{1}{11} - \frac{5}{22} \left.\right)\)

         \(D = \frac{4}{9} : \left(\right. \frac{1}{15} - \frac{10}{15} \left.\right) + \frac{4}{9} : \left(\right. \frac{2}{22} - \frac{5}{22} \left.\right)\)

         \(D = \frac{4}{9} : \frac{- 3}{5} + \frac{4}{9} : \frac{- 3}{22}\)

         \(D = \frac{4}{9} . \frac{- 5}{3} + \frac{4}{9} . \frac{- 22}{3}\)

         \(D = \frac{4}{9} . \left(\right. \frac{- 5}{3} + \frac{- 22}{3} \left.\right)\)

         \(D = \frac{4}{9} . \left(\right. - 9 \left.\right)\)

         \(D = - 4\)

A=(3−41​+23​)−(5+31​−65​)−(6−47​+32​)⇒A=3−41​+23​−5−31​+65​−6+47​−32​⇒A=(3−5−6)−(41​+47​)+(23​+65​−32​)⇒A=−8−23​+35​=−647​.B=0,5+31​+0,4+75​+61​−354​+411​

\(\Rightarrow B = \left(\right. 0 , 5 + 0 , 4 \left.\right) + \left(\right. \frac{1}{3} + \frac{1}{6} \left.\right) + \left(\right. \frac{5}{7} - \frac{4}{35} \left.\right) + \frac{1}{41} \Rightarrow B = \frac{9}{10} + \frac{1}{2} + \frac{3}{5} + \frac{1}{41} \Rightarrow B = 2 + \frac{1}{41} \Rightarrow B = \frac{83}{41} .\)

a) A=(13+23)−(815+715)+(−17+117)=1−1+1=1A=(13+23)−(815+715)+(−17+117)=1−1+1=1;
b) B=(0.25−114)+(35+25)−18B=(0.25−114)+(35+25)−18