[latex] \left \{ {{\sqrt{x/y} - \sqrt{y/x} = 3/2} \atop {x+y+xy=9}} \right[/latex]

[latex]\frac{x}{y}=a\\\\ \sqrt{a} - \sqrt{\frac{1}{a}}=\frac{3}{2}\\ \sqrt{a}-\frac{1}{\sqrt{a}}=\frac{3}{2}\\ \frac{a-1}{\sqrt{a}}=\frac{3}{2}\\ 2a-2=3\sqrt{a}\\ 4a^2-8a+4=9a\\ 4a^2-17a+4=0\\ D=15^2\\ a=\frac{17+15}{8}=4\\ a=\frac{17-15}{8}=\frac{1}{4}\\ x=4y\\ y=4x\\\\ 5y+4y^2=9\\ 5x+4x^2=9\\\\ 4y^2+5y-9=0\\ D=25+4*4*9=13^2\\ y=\frac{-5+13}{8}=1\\ y=\frac{-5-13}{8}=-\frac{9}{4}\\ x=4\\ x=-9[/latex]