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ContourPlot3D[{(x*y)/(x^2+y^2)==z}, {x,-2,2},{y,-2,2},{z,-1,1}, MeshFunctions->{#3&},AxesLabel->{x,y,z}]

ContourPlot3D[{0==z, (x*y)/(x^2+y^2)==z}, {x,-2,2},{y,-2,2},{z,-1,1}, MeshFunctions->{#3&},AxesLabel->{x,y,z}, ContourStyle->{Red,Green}]