Thực hiện phép tính một cách hợp lí:

k) \(\left( {\frac{4}{5} + \frac{{ - 9}}{7}} \right):\frac{{2\,\,024}}{{2\,\,025}} + \left( {\frac{{ - 5}}{7} - \frac{{ - 6}}{5}} \right):\frac{{2\,\,024}}{{2\,\,025}}.\)

a) \[\frac{{\frac{3}{4} + \frac{3}{5} + \frac{3}{7} - \frac{3}{{11}}}}{{\frac{6}{4} + \frac{6}{5} + \frac{6}{7} - \frac{6}{{11}}}} = \frac{{3 \cdot \left( {\frac{1}{4} + \frac{1}{4} + \frac{1}{7} - \frac{1}{{11}}} \right)}}{{6 \cdot \left( {\frac{1}{4} + \frac{1}{4} + \frac{1}{7} - \frac{1}{{11}}} \right)}} = \frac{3}{6} = \frac{1}{2}.\]

h) \[\frac{7}{{13}} \cdot 1\frac{{14}}{{31}} - \frac{{37}}{{31}}:\frac{{13}}{7} + \frac{7}{{13}}\]

\( = \frac{7}{{13}} \cdot \frac{{45}}{{31}} - \frac{{37}}{{31}} \cdot \frac{7}{{13}} + \frac{7}{{13}}\)

\[ = \frac{7}{{13}} \cdot \left( {\frac{{45}}{{31}} - \frac{{37}}{{31}} + 1} \right)\]