$\dfrac{2x}{3}=\dfrac{3y}{4}=\dfrac{4z}{5}$
$↔\dfrac{x}{\dfrac{3}{2}}=\dfrac{y}{\dfrac{4}{3}}=\dfrac{z}{\dfrac{5}{4}}$
Áp dụng tính chất dãy tỉ số bằng nhau:
$\dfrac{x}{\dfrac{3}{2}}=\dfrac{y}{\dfrac{4}{3}}=\dfrac{z}{\dfrac{5}{4}}=\dfrac{x+y+z}{\dfrac{3}{2}+\dfrac{4}{3}+\dfrac{5}{4}}=\dfrac{38}{\dfrac{49}{12}}=\dfrac{456}{49}$
$→\dfrac{x}{\dfrac{3}{2}}=\dfrac{456}{49}→x=\dfrac{684}{49}$
$\dfrac{y}{\dfrac{4}{2}}=\dfrac{456}{49}→y=\dfrac{608}{49}$
$\dfrac{z}{\dfrac{4}{5}}=\dfrac{456}{49}→z=\dfrac{570}{49}$
Vậy $(x,y,z)=(\dfrac{684}{49},\dfrac{608}{49},\dfrac{570}{49})$
