\(\dfrac{1}{7}.\dfrac{5}{9}+\dfrac{5}{7}.\dfrac{1}{9}+\dfrac{5}{9}.\dfrac{3}{7}=\dfrac{5}{9}.\left(\dfrac{1}{7}+\dfrac{3}{7}\right)+\dfrac{5}{7}.\dfrac{1}{9}\\ =\dfrac{5}{9}.\dfrac{4}{7}+\dfrac{5}{7}.\dfrac{1}{9}=\dfrac{20}{63}+\dfrac{5}{63}=\dfrac{25}{63}\)
\(\dfrac{1}{7}.\dfrac{5}{9}+\dfrac{5}{7}.\dfrac{5}{9}+\dfrac{5}{9}.\dfrac{3}{7}\)
\(=\dfrac{5}{9}.\left(\dfrac{1}{7}+\dfrac{5}{7}+\dfrac{3}{7}\right)\)
\(=\dfrac{5}{9}.\dfrac{9}{7}\)
\(=\dfrac{5}{7}\)
\(\dfrac{1}{7}.\dfrac{5}{9}+\dfrac{5}{7}.\dfrac{1}{9}+\dfrac{5}{9}.\dfrac{3}{7}\)
\(=\dfrac{5}{9}.\left(\dfrac{1}{7}+\dfrac{3}{7}\right)+\dfrac{5}{7}.\dfrac{1}{9}\)
\(=\dfrac{5}{9}.\dfrac{4}{7}+\dfrac{5}{63}\)
\(=\dfrac{20}{63}+\dfrac{5}{63}=\dfrac{25}{63}\)
