Please check this very carefully before you even think of trusting this, make certain that I have not made any mistake in this. If I have made a mistake then perhaps you can guess what my thinking was and be able to correct this.

x[0]=1;x[1]=1;x[n_]:=x[n-2]/(2+x[n-1]);xtbl=Table[x[n],{n,0,10}]
y[0]=1;y[1]=1;y[n_]:=6/5 y[n-1]/(1+y[n-2]);ytbl=Table[y[n],{n,0,10}]
ListPlot[{xtbl,ytbl}]

Since the first two points of the two sequences are the same, the color of one of the dots will lay over the other dot for those, but the points are distinct for the rest of the sequences and thus the points will be separate.