Plot3D[((((((x^2)-(y^2))/((x^2)+(y^2)))))^2),{x,-1,1},{y,-1,1}]

f[x_,y_]:=(((x^2)y)/((x^4)+(y^2)))

c[t_]:={0,0}+t{1,m}

m=.5;

ParametricPlot[c[t],{t,0,1},AspectRatio->Automatic,PlotRange->{0,1}]

fun=Plot3D[f[x,y],{x,-1,1},{y,-1,1},PlotPoints->100];
curv=ParametricPlot3D[{Sequence@@c[t],f[Sequence@@c[t]]},{t,0,1}];
Show[{fun,curv}]