[tex] \frac{1}{2x} + \frac{1}{3y} = \frac{1}{4}|\cdot 12xy \\
6y+4x=3xy\\
3xy-6y=4x\\
y(3x-6)=4x\\
y= \frac{4x}{3x-6} \in Z=>3y\in Z=>\frac{12x}{3x-6} \in Z=>
\frac{4(3x-6)+24}{3x-6} \in Z=>\\
4+ \frac{8}{x-2} \in Z=>\frac{8}{x-2} \in Z\\
x-2=\pm1;\pm2;\pm4;\pm8\\
x=3=>y=4\\
x=6=>y=2[/tex]
