Question

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Answer 1

a/b+a/c=5/8

ac+ab/bc=5/8

a(b+c)/bc=5/8

b/c=2/3

b=2c/3

a(b+c)/bc=5/8

a/b * b+c/c=5/8

a/b=5/8 : b+c/c

a/b=5c/8(b+c)

a/b=5c/8(2c/3+c)=5c/8*(2c+3c)/3=5c*3/8*5c=3/8

Answer 2

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