Ta có:
\(\frac{x}{3}=\frac{y}{4}\Rightarrow\frac{1}{5}.\frac{x}{3}=\frac{1}{5}.\frac{y}{4}\Rightarrow\frac{x}{15}=\frac{y}{20}\)
\(\frac{y}{5}=\frac{z}{6}\Rightarrow\frac{1}{4}.\frac{y}{5}=\frac{1}{4}.\frac{z}{6}\Rightarrow\frac{y}{20}=\frac{z}{24}\)
\(\Rightarrow\frac{x}{15}=\frac{y}{20}=\frac{z}{24}=k\Rightarrow\left\{{}\begin{matrix}x=15k\\y=20k\\z=24k\end{matrix}\right.\)
\(\Rightarrow P=\frac{2x+3y+4z}{3x+4y+2z}=\frac{2.15k+3.20k+4.24k}{3.15k+4.20k+2.24k}=\frac{30k+60k+96k}{45k+80k+48k}=\frac{186k}{173k}=\frac{186}{173}\)
