[tex] \frac{x}{y} = \frac{3}{2} [/tex]
[tex]2x = 3y[/tex]
[tex]x = \frac{3y}{2} [/tex]
[tex] \frac{3x + y}{2x + 3y} = \frac{3 \times \frac{3y}{2} + y}{2 \times \frac{3y}{2} + 3y} = \frac{ \frac{9y}{2} + y }{ \frac{6y}{2} + 3y } [/tex]
[tex] = \frac{ \frac{9y}{2} + \frac{2y}{2} }{ 3y + 3y} = \frac{ \frac{11y}{2} }{6y} = \frac{11y}{2} \times \frac{1}{6y} = \frac{11y}{12y} = \frac{11}{12} [/tex]
