a)
[tex]\dfrac{3}{4}+\dfrac{4}{3}=\dfrac{3\cdot3}{4\cdot3}+\dfrac{4\cdot4}{3\cdot4}=\dfrac{9}{12}+\dfrac{16}{12}=\dfrac{25}{12}=\boxed{2\dfrac{1}{12}}\\[/tex]
b)
[tex]\dfrac{1}{5}+\dfrac{3}{7}=\dfrac{1\cdot7}{5\cdot7}+\dfrac{3\cdot5}{7\cdot5}=\dfrac{7}{35}+\dfrac{15}{35}=\boxed{\frac{22}{35}}\\[/tex]
c)
[tex]6\dfrac{2}{3}+5\dfrac{5}{8}=6\dfrac{2\cdot8}{3\cdot8}+5\dfrac{5\cdot3}{8\cdot3}=6\dfrac{16}{24}+5\dfrac{15}{24}=11\dfrac{31}{24}=\boxed{12\dfrac{7}{24}}\\[/tex]
d)
[tex]4\dfrac{3}{5}+4\dfrac{3}{4}=4\dfrac{3\cdot4}{5\cdot4}+4\dfrac{3\cdot5}{4\cdot5}=4\dfrac{12}{20}+4\dfrac{15}{20}=8\dfrac{27}{20}=\boxed{9\dfrac{7}{20}}\\[/tex]
