a: \(A=\left(3-\dfrac{3}{4}+\dfrac{2}{3}\right)-\left(2+\dfrac{4}{3}-\dfrac{3}{2}\right)-\left(1-\dfrac{7}{3}-\dfrac{9}{2}\right)\)
\(=3-\dfrac{3}{4}+\dfrac{2}{3}-2-\dfrac{4}{3}+\dfrac{3}{2}-1+\dfrac{7}{3}+\dfrac{9}{2}\)
\(=\left(3-2-1\right)+\left(-\dfrac{3}{4}+\dfrac{3}{2}+\dfrac{9}{2}\right)+\left(\dfrac{2}{3}-\dfrac{4}{3}+\dfrac{7}{3}\right)\)
\(=0+\left(-\dfrac{3}{4}+6\right)+\dfrac{5}{3}\)
\(=\dfrac{21}{4}+\dfrac{5}{3}=\dfrac{63}{12}+\dfrac{20}{12}=\dfrac{83}{12}\)
b: \(B=-\dfrac{1}{3}-\dfrac{8}{35}+\dfrac{-2}{9}-\dfrac{1}{135}+\dfrac{4}{5}+\dfrac{-4}{9}+\dfrac{3}{7}\)
\(=\left(-\dfrac{8}{35}+\dfrac{4}{5}+\dfrac{3}{7}\right)+\left(-\dfrac{1}{3}-\dfrac{2}{9}-\dfrac{4}{9}-\dfrac{1}{135}\right)\)
\(=\left(-\dfrac{8}{35}+\dfrac{28}{35}+\dfrac{15}{35}\right)+\left(-\dfrac{45}{135}-\dfrac{30}{135}-\dfrac{60}{135}-\dfrac{1}{135}\right)\)
\(=1+\dfrac{-135}{135}-\dfrac{1}{135}=-\dfrac{1}{135}\)
c: \(C=\dfrac{0,75+0,6-\dfrac{3}{7}-\dfrac{3}{13}}{2.75+2,2-\dfrac{11}{7}-\dfrac{11}{13}}\)
\(=\dfrac{3\left(0,25+0,2-\dfrac{1}{7}-\dfrac{1}{13}\right)}{11\left(0,25+0,2-\dfrac{1}{7}-\dfrac{1}{13}\right)}=\dfrac{3}{11}\)
d: \(D=\dfrac{-\dfrac{2}{3}+\dfrac{3}{4}-2}{\dfrac{2}{3}-\dfrac{3}{4}-2}\cdot\dfrac{-\dfrac{2}{3}-\dfrac{3}{4}-2}{\dfrac{2}{3}+\dfrac{3}{4}+2}\)
\(=\dfrac{-\dfrac{8}{12}+\dfrac{9}{12}-\dfrac{24}{12}}{\dfrac{8}{12}-\dfrac{9}{12}-\dfrac{24}{12}}\cdot\dfrac{-\left(\dfrac{2}{3}+\dfrac{3}{4}+2\right)}{\dfrac{2}{3}+\dfrac{3}{4}+2}\)
\(=\dfrac{-23}{12}:\dfrac{-25}{12}\cdot\left(-1\right)=\dfrac{23}{25}\cdot\left(-1\right)=-\dfrac{23}{25}\)
a)
A=(\(\dfrac{36}{12}\) - \(\dfrac{9}{12}\)+\(\dfrac{8}{12}\)) - ( \(\dfrac{24}{12}\) + \(\dfrac{16}{12}\) - \(\dfrac{18}{12}\) ) - ( \(\dfrac{12}{12}\) - \(\dfrac{21}{12}\) - \(\dfrac{54}{12}\))
= \(\dfrac{19}{12}\) - \(\dfrac{22}{12}\) - \(\dfrac{-63}{12}\)
= 5
