[tex] \frac{x}{y} \div \frac{2}{3} = \frac{3}{4}\\\\ \frac{x}{y} \times
\frac{3}{2} = \frac{3}{4}\\\\ \frac{3x}{2y}
=\frac{3}{4}\\\\\\3x=3\\x=1\\\\\2y=4\\y=2\\\\\frac{x}{y} =
\frac{1}{2}\\\\\\\boxed{\bf{\frac{1}{2}}}\div\frac{2}{3} =
\frac{3}{4}[/tex]
Hope this helps!! If you have any other questions or would like further explanation just let me know! :)