smc

To clear out the fractions, we multiply both sides of the equation by $xy$ to get $2y+3x=\frac{xy}{2}$, or $4y+6x=xy$. From this, we have $4y=xy-6x$. We can factor an $x$ out of the RHS, and so $4y=x(y-6)⟹\frac{4y}{y-6}=x,\boxed{\frac{4y}{y-6}=x}$.