Plotting – Function for the domain of the differential equation

Domain of d.e y = f (x, y) is domain[f] Union domain[1/f],
I want to create a function in Mathematica that gives domain of every d.e and plots them.

    DomainDJ[f_, vars_] : =
union[FunctionDomain[f, vars], FunctionDomain[1/f, vars]];

This function gives us domain of d.e, with regionplot we can plot that RegionPlot[DomainDJ, {x, -2, 2}, {y, -2, 2}]

For example, d.e y = (y * log[y]) / x If we use this function, we will get a good representation, but we can not see that the region point (0,1) is assumed.

I have defined a new function

PlotDomainDJSP[f_, vars_, sp_] : =
module[{pddj = {}}, spt = Transpose[sp];
amine = min[spt[[1]]];
amax = max[spt[[1]]];
bmin = min[spt[[2]]];
bmax = max[spt[[2]]];
aamin = min[{0, amin}];
aamax = max[{-aamin, amax}];
bbmin = min[{0, bmin}];
bbmax = max[{-bbmin, bmax}];
To the[I=1i[I=1i[i=1i[i=1i<= Dimensions[sp][[1]], i++, 
    pddj = Append[pddj, 
      ParametricPlot[{aamin - 1 + (spt[[1, i]] - aamin + 1)*t, 
        spt[[2, i]]}, {t, 0, 1}, PlotStyle -> {Red, dashing[Tiny]}]];
pddj = Append[pddj, 
      ParametricPlot[{spt[[1, i]],
bbmin - 1 + (sec[[2, i]]- bbmin + 1) * t}, {t, 0, 1},
PlotStyle -> {red, dashing[Tiny]}]];
pddj = Append[pddj, 
      ParametricPlot[{((aamax - aamin + 2)/300) Cos[
           t], ((aamax - aamine + 2) / 300) Sin
2 Pi}, PlotStyle -> Red]]];
df = DomainDJ[f, vars];
rpdj =
RegionPlot[
     df, {x, aamin - 1, aamax + 1}, {y, bbmin - 1, bbmax + 1}];
show[{rpdj, pddj}]];

which shows us everything nicely, but the first problem is that you have to manually get points that give 0/0. My first question is how to set in this program that we get 0/0 no manual point.

Then my next question is: Can I merge this 2x function, for example, if we have no dots in d.e specifying the first function of case 0/0 program use? If we get the second function with point 0/0 program use, how would this be done?

I would like a compact program feature that will give us the VISUAL domain of d.e, so maybe with this my idea or something else, maybe it can be a lot easier (but visually with 0/0 too!)