Ta có : \(\dfrac{x}{y}=\dfrac{3}{4};\dfrac{y}{z}=\dfrac{5}{6}\)
\(\Rightarrow4x=3y;6y=5z\)
\(\Leftrightarrow8x=6y=5z.\)
\(\Rightarrow y=\dfrac{8x}{6}=\dfrac{4}{3}x\)
Thay vào A ta có :
\(A=\dfrac{2x+3y+5z}{y+5z}=\dfrac{2x+4x+8x}{\dfrac{4}{3}x+8x}=\dfrac{3}{2}.\)