Ta có: $\frac{x}{3}$ = $\frac{y}{4}$ ⇒ x = $\frac{3y}{4}$
$\frac{z}{6}$ = $\frac{y}{9}$ ⇒ z = $\frac{6y}{9}$ = $\frac{2y}{3}$
Ta có:
M = $\frac{2x+3y+4z}{3x+4y+5z}$ = $\frac{2.\frac{3y}{4}+3y+4.\frac{2y}{3}}{3.\frac{3y}{4}+4y+5.\frac{2y}{3}}$ = $\frac{y.(2.\frac{3}{4}+3+4.\frac{2}{3})}{y.(3.\frac{3}{4}+4+5.\frac{2}{3})}$ = $\frac{2.\frac{3}{4}+3+4.\frac{2}{3}}{3.\frac{3}{4}+4+5.\frac{2}{3}}$
= $\frac{\frac{43}{6}}{\frac{115}{12}}$ = $\frac{86}{115}$
