Connecting two wireless routers

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I have two wireless routers, WRT54G v. 2 and BEFW11S4 v. 4. I'll call
them A and B respectively. Router A is connected to the a modem which
connects to the internet and one computer, running windows XP, is
hardwired to it. Router B is in a different room connecting two
computers, one running linux connecting wirelessly and the other
windows XP hardwired. A wireless game adapter is plugged into router
B's internet port and connects to router A. My problem is that I
cannot see the computers on my network from the computer connected to
router B, nor can I share printers or files. I've heard about WDS but,
correct me if I'm wrong, I don't think that will work in my case since
router B is an older different model than the first and plus, I don't
want to cut my connection speed in half. Any support would be greatly
appreciated.

.

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