extend airport extreme network via ethernet to airport express (special case)
This question has been asked many times on the forum, and answered many times, but I have a special case and would like to know if it can be made to work.
As you can see, the issue is that the LAN port of the Extreme is not connected back to the switch, I've only connected the WAN port of the Extreme to the switch. Therefore the express doesn't get an IP over the CAT5e cable coming from the switch, and will only extend wirelessly. The reason I don't make that connection is because the switch/modem is in the basement, the Extreme is on the second floor, the express is on the far side of the first floor, and I don't want to run another cable through the house.
First question is, can the given topology be made to work?
If the answer is no, then would it work to put an additional switch on the second floor like the following?
Thanks!
airport extreme-OTHER, OS X Mavericks (10.9.5)