\(\dfrac{5}{9}\cdot\dfrac{7}{13}+\dfrac{5}{9}\cdot13-\dfrac{5}{9}\cdot\dfrac{3}{13}\)
\(=\dfrac{5}{9}\cdot\left(\dfrac{7}{13}-\dfrac{3}{13}+13\right)\)
\(=\dfrac{5}{9}\cdot\left(\dfrac{4}{13}+13\right)\)
\(=\dfrac{5}{9}\cdot\dfrac{173}{13}\)
\(=\dfrac{865}{117}\)
=5/9(7/13+13-3/13)
=5/9*(13+4/13)
=5/9*173/13=865/117