Thực hiện phép tính: \(\frac{5}{9} \cdot \frac{7}{{13}} + \frac{5}{9} \cdot \frac{9}{{13}} + \frac{3}{{13}} \cdot \frac{{ - 5}}{9}\)

* Hướng dẫn giải

\(\frac{5}{9} \cdot \frac{7}{{13}} + \frac{5}{9} \cdot \frac{9}{{13}} + \frac{3}{{13}} \cdot \frac{{ - 5}}{9}\)

\(\begin{array}{l}\,\,\,\,\frac{5}{9} \cdot \frac{7}{{13}} + \frac{5}{9} \cdot \frac{9}{{13}} + \frac{3}{{13}} \cdot \frac{{ - 5}}{9}\\ = \frac{5}{9} \cdot \frac{7}{{13}} + \frac{5}{9} \cdot \frac{9}{{13}} - \frac{3}{{13}} \cdot \frac{5}{9}\\ = \frac{5}{9} \cdot \left( {\frac{7}{{13}} + \frac{9}{{13}} - \frac{3}{{13}}} \right)\\ = \frac{5}{9} \cdot \left( {\frac{{16}}{{13}} - \frac{3}{{13}}} \right)\\ = \frac{5}{9} \cdot \frac{{13}}{{13}}\\ = \frac{5}{9}\end{array}\)