How to induce plot() to detect singularities ?

[Emmanuel Charpentier]

let the real function 

f(x)=(2-sqrt(x+1))/(x-3)

Sage has no difficulty finding the limits at x=-1 and x=3. However, I am unable to get plot to detect these singularities :

plot((2-sqrt(x+1))/(x-3),[x,-1,6],figsize=4,detect_poles=True)

gives me a continuous curve between -1 and 6 with no marking whatsoever at -1 and 6.

Can someone suggest a more-or-less automated way to get

1) a curve segment between abcissae -1 and 3 with some marker excluding the point at abcissa 3?

2) a curve segment between 3 an 6 with a marker at abcissa 3

I want to emphasize that the function is not defined at 3 and (for real values), not defined for x<0

Bonus points (just kidding :-) for the representation of the complex (multivalued) function

f(z)=(2-sqrt(z+1))/(z-3)

where sqrt(t) is a root r of r^2=t....