Đáp án:

$\begin{array}{l}
a)A = \dfrac{{ - 13}}{6}\\
b)B = \dfrac{{ - 23}}{{30}}
\end{array}$

Giải thích các bước giải:

$\begin{array}{l}
a)A = \left( {3 + \dfrac{1}{2} - \dfrac{2}{3}} \right) - \left( {2 - \dfrac{2}{3} + \dfrac{5}{2}} \right) - \left( {5 - \dfrac{5}{2} - \dfrac{4}{3}} \right)\\
 = 3 + \dfrac{1}{2} - \dfrac{2}{3} - 2 + \dfrac{2}{3} - \dfrac{5}{2} - 5 + \dfrac{5}{2} + \dfrac{4}{3}\\
 = \left( {3 - 2 - 5} \right) + \left( {\dfrac{1}{2} - \dfrac{5}{2} + \dfrac{5}{2}} \right) + \left( {\dfrac{4}{3} - \dfrac{2}{3} + \dfrac{2}{3}} \right)\\
 =  - 4 + \dfrac{1}{2} + \dfrac{4}{3}\\
 =  - \dfrac{{13}}{6}\\
b)B = \dfrac{1}{{90}} - \dfrac{1}{{72}} - \dfrac{1}{{56}} - \dfrac{1}{{42}} - \dfrac{1}{{30}} - \dfrac{1}{{20}} - \dfrac{1}{6} - \dfrac{1}{2}\\
 = \dfrac{1}{{9.10}} - \dfrac{1}{{8.9}} - \dfrac{1}{{7.8}} - \dfrac{1}{{6.7}} - \dfrac{1}{{5.6}} - \dfrac{1}{{4.5}} - \dfrac{1}{{2.3}} - \dfrac{1}{{1.2}}\\
 = \dfrac{1}{9} - \dfrac{1}{{10}} - \left( {\dfrac{1}{8} - \dfrac{1}{9}} \right) - \left( {\dfrac{1}{7} - \dfrac{1}{8}} \right) - \left( {\dfrac{1}{6} - \dfrac{1}{7}} \right) - \left( {\dfrac{1}{5} - \dfrac{1}{6}} \right) - \left( {\dfrac{1}{4} - \dfrac{1}{5}} \right) - \left( {\dfrac{1}{2} - \dfrac{1}{3}} \right) - \dfrac{1}{2}\\
 =  - \dfrac{1}{{10}} - \dfrac{1}{4} - \dfrac{1}{2} + \dfrac{1}{3} - \dfrac{1}{2}\\
 = \dfrac{1}{3} - \dfrac{1}{{10}} - \left( {\dfrac{1}{4} + \dfrac{1}{2} + \dfrac{1}{2}} \right)\\
 = \dfrac{7}{{30}} - 1\\
 = \dfrac{{ - 23}}{{30}}
\end{array}$