Thực hiện phép tính một cách hợp lí:

c) \[\frac{{\frac{1}{2} \cdot \frac{5}{{17}} - \frac{{13}}{{14}} \cdot \frac{5}{{17}} + \frac{{15}}{{238}}}}{{ - \frac{{20}}{{68}} + \frac{{26}}{{14}} \cdot \frac{5}{{17}} - \frac{5}{{119}}}}.\]

k) \(\left( {\frac{1}{4} + \frac{{ - 5}}{{13}}} \right) + \left( {\frac{2}{{11}} + \frac{{ - 8}}{{13}} + \frac{3}{4}} \right)\)

\( = \frac{1}{4} + \frac{{ - 5}}{{13}} + \frac{2}{{11}} + \frac{{ - 8}}{{13}} + \frac{3}{4}\)

\( = \left( {\frac{1}{4} + \frac{3}{4}} \right) + \left( {\frac{{ - 5}}{{13}} + \frac{{ - 8}}{{13}}} \right) + \frac{2}{{11}}\)

\( = \frac{4}{4} + \frac{{ - 13}}{{13}} + \frac{2}{{11}}\)

d) \( - \frac{3}{7} \cdot \frac{{12}}{{13}} + \frac{3}{7} \cdot \left( { - \frac{1}{{13}}} \right) + \frac{5}{{14}}\)

\( = \frac{3}{7} \cdot \frac{{ - 12}}{{13}} + \frac{3}{7} \cdot \left( { - \frac{1}{{13}}} \right) + \frac{5}{{14}}\)

\[ = \frac{3}{7} \cdot \left[ {\frac{{ - 12}}{{13}} + \left( { - \frac{1}{{13}}} \right)} \right] + \frac{5}{{14}}\]

\[ = \frac{3}{7} \cdot \frac{{ - 13}}{{13}} + \frac{5}{{14}}\]

\[ = \frac{3}{7} \cdot \left( { - 1} \right) + \frac{5}{{14}}\]\[ = \frac{{ - 3}}{7} + \frac{5}{{14}}\]