[tex]\dfrac{3\frac{1}{2}}{5}+\dfrac{\frac{14}{3}}{2}=3\dfrac{1}{2}\cdot\dfrac{1}{5}+\dfrac{14}{3}\cdot\dfrac{1}{2}=\dfrac{3\cdot2+1}{2}\cdot\dfrac{1}{5}+\dfrac{7}{3}\cdot\dfrac{1}{1}\\\\=\dfrac{7}{2}\cdot\dfrac{1}{5}+\dfrac{7}{3}=\dfrac{7}{10}+\dfrac{7}{3}=\dfrac{7\cdot3}{10\cdot3}+\dfrac{7\cdot10}{3\cdot10}=\dfrac{21}{30}+\dfrac{70}{30}\\\\=\dfrac{91}{30}=3\dfrac{1}{30}[/tex]
