Đáp án:
$\begin{array}{l}
\dfrac{1}{{2.3}} - \dfrac{8}{{3.5}} + \dfrac{4}{{5.9}} - \dfrac{{22}}{{9.13}} + \dfrac{{31}}{{13.18}}\\
= \dfrac{{3 - 2}}{{2.3}} - \dfrac{{3 + 5}}{{3.5}} + \dfrac{{9 - 5}}{{5.9}} - \dfrac{{9 + 13}}{{9.13}} + \dfrac{{13 + 18}}{{13.18}}\\
= \left( {\dfrac{1}{2} - \dfrac{1}{3}} \right) - \left( {\dfrac{1}{3} + \dfrac{1}{5}} \right) + \left( {\dfrac{1}{5} - \dfrac{1}{9}} \right)\\
- \left( {\dfrac{1}{9} + \dfrac{1}{{13}}} \right) + \left( {\dfrac{1}{{13}} + \dfrac{1}{{18}}} \right)\\
= \dfrac{1}{2} - \dfrac{1}{3} - \dfrac{1}{3} - \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{9} - \dfrac{1}{9} - \dfrac{1}{{13}} + \dfrac{1}{{13}} + \dfrac{1}{{18}}\\
= \dfrac{1}{2} + \dfrac{1}{{18}}\\
= \dfrac{{10}}{{18}} = \dfrac{5}{9}
\end{array}$
