\(\dfrac{3}{5}+\dfrac{5}{9}:\dfrac{4}{6}=\dfrac{3}{5}+\dfrac{5}{9}\text{×}\dfrac{6}{4}=\dfrac{3}{5}+\dfrac{5}{9}\text{×}\dfrac{3}{2}=\dfrac{3}{5}+\dfrac{5}{6}=\dfrac{18}{30}+\dfrac{25}{30}=\dfrac{43}{30}\)
\(=\dfrac{3}{5}+\dfrac{30}{36}=\dfrac{3}{5}+\dfrac{15}{18}=\dfrac{43}{30}\)