[tex]\dfrac{a}{b}+\dfrac{a}{c}=\dfrac{5}{8},\quad \dfrac{b}{c}=\dfrac{2}{3}\\ \\ \dfrac{a}{b} = t\Rightarrow a = bt \\ \\ \Rightarrow t+\dfrac{bt}{c} = \dfrac{5}{8} \Rightarrow t+t\cdot \dfrac{b}{c} = \dfrac{5}{8} \Rightarrow t+t\cdot \dfrac{2}{3} = \dfrac{5}{8} \Big|\cdot 3\cdot 8 \Rightarrow\\ \\ \Rightarrow 24t+16t = 15 \Rightarrow 40t = 15 \Rightarrow t = \dfrac{15}{40} \Rightarrow t = \dfrac{3}{8} \Rightarrow \boxed{\dfrac{a}{b} = \dfrac{3}{8}}[/tex]
