[tex]\dfrac{3x-5y}{2x+3y} =\dfrac{2}{3} \Rightarrow \dfrac{\dfrac{1}{y}}{\dfrac{1}{y}}\cdot \dfrac{3x-5y}{2x+3y} =\dfrac{2}{3}\Rightarrow \dfrac{\dfrac{3x}{y}-5}{\dfrac{2x}{y}+3} =\dfrac{2}{3} \\\\\\\text{Notez:}\quad \dfrac{x}{y} = t \Rightarrow \dfrac{3t-5}{2t+3} = \dfrac{2}{3} \Rightarrow 3(3t-5) = 2(2t+3) \Rightarrow \\ \\\\ \Rightarrow 9t-15=4t+6 \Rightarrow 5t = 21 \Rightarrow t = \dfrac{21}{5} \Rightarrow \boxed{\dfrac{x}{y} = \dfrac{21}{5}}[/tex]
