\(\dfrac{3x-y}{x+y}=\dfrac{3}{4}\)
\(\Rightarrow4\left(3x-y\right)=3\left(x+y\right)\)
\(\Rightarrow12x-4y=3x+3y\)
\(\Rightarrow12x-4y-3y=3x\)
\(\Rightarrow12x-7y=3x\)
\(\Rightarrow12x-3x=7y\)
\(\Rightarrow9x=7y\)
\(\Rightarrow\dfrac{x}{7}=\dfrac{y}{9}\)
\(\Rightarrow\dfrac{x}{y}=\dfrac{7}{9}\)