Ta có : \(\frac{3x-2y}{4}=\frac{2z-4x}{3}=\frac{4y-3z}{2}\)
=> \(\frac{12x-8y}{16}=\frac{6z-12x}{9}=\frac{8y-6z}{4}=\frac{12x-8y+6z-12x+8y-6x}{16+9+4}=0\)
=> \(\hept{\begin{cases}12x-8y=0\\6z-12x=0\\8y-6z=0\end{cases}\Rightarrow\hept{\begin{cases}3x-2y=0\\2z-4x=0\\4y-3z=0\end{cases}\Rightarrow}\hept{\begin{cases}\frac{x}{2}=\frac{y}{3}\\\frac{z}{4}=\frac{x}{2}\\\frac{y}{3}=\frac{z}{4}\end{cases}}}\)
\(\Rightarrow\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\)