Ta có :
\(\frac{x}{3}=\frac{y}{4}\)\(\Leftrightarrow\)\(\frac{x}{15}=\frac{y}{20}\) \(\left(1\right)\)
\(\frac{x}{5}=\frac{z}{6}\)\(\Leftrightarrow\)\(\frac{x}{15}=\frac{z}{18}\) \(\left(2\right)\)
Từ (1) và (2) suy ra \(\frac{x}{15}=\frac{y}{20}=\frac{z}{18}\)
Đặt \(\frac{x}{15}=\frac{y}{20}=\frac{z}{18}=k\)\(\Rightarrow\)\(\hept{\begin{cases}x=15k\\y=20k\\z=18k\end{cases}}\)
\(\Rightarrow\)\(M=\frac{2x+3y+4z}{3x+4y+5z}=\frac{30k+60k+72k}{45k+80k+90k}=\frac{k\left(30+60+72\right)}{k\left(45+80+90\right)}=\frac{162k}{215k}=\frac{162}{215}\)
Vậy \(M=\frac{162}{215}\)
Chúc bạn học tốt ~