ContourPlot[(x^2-2 y^2)/(x^2+y^2),{x,-2,2},{y,-2,2},ContourShading->False,ContourLabels->True]

ContourPlot[((x y)/(2 (x^2)+3 (y^2))),{x,-2,2},{y,-2,2},ContourShading->False,ContourLabels->True]

ContourPlot[((x y)/((x^2)+(y^2))),{x,-2,2},{y,-2,2},ContourShading->False,ContourLabels->True]