3z là 3x phải k :v
\(\frac{x}{3}=\frac{y}{4}\Rightarrow\frac{x}{15}=\frac{y}{20}\)
\(\frac{y}{5}=\frac{z}{6}\Rightarrow\frac{y}{20}=\frac{z}{24}\)
nên :
\(\frac{x}{15}=\frac{y}{20}=\frac{z}{24}\)
\(\Rightarrow\hept{\begin{cases}\frac{3x}{45}=\frac{4y}{80}=\frac{5z}{120}\\\frac{4x}{60}=\frac{5y}{100}=\frac{6z}{144}\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}\frac{3x+4y+5z}{45+80+120}=\frac{x}{15}=\frac{y}{20}=\frac{z}{24}\\\frac{4x+5y+6z}{60+100+144}=\frac{x}{15}=\frac{y}{20}=\frac{z}{24}\end{cases}}\)
\(\Rightarrow\frac{3x+4y+5z}{245}=\frac{4x+5y+6z}{304}\)
\(\Rightarrow\frac{3x+4y+5z}{4x+5y+6z}=\frac{245}{304}\)
\(\Rightarrow M=\frac{245}{304}\)
bài này đặt k ez hơn : )
\(\hept{\begin{cases}\frac{x}{3}=\frac{y}{4}\Rightarrow\frac{x}{15}=\frac{y}{20}\\\frac{y}{5}=\frac{z}{6}\Rightarrow\frac{y}{20}=\frac{z}{24}\end{cases}}\Rightarrow\frac{x}{15}=\frac{y}{20}=\frac{z}{24}\)
đặt \(k=\frac{x}{15}=\frac{y}{20}=\frac{z}{24}\Rightarrow x=15k,y=20k,z=24k\)
\(\Rightarrow M=\frac{3x+4y+5z}{4x+5y+6z}=\frac{3.15k+4.20k+5.24k}{4.15k+5.20k+6.24k}=\frac{245}{304}\)