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If you are going to hang a stand-alone / separate router like the Airport off of the gateway device, and the gateway is not in *bridge mode*, you are cascading 2 routing devices which results in an undesirable "double NAT" condition on your home network.
Google "double NAT" for info about it's potential pitfalls.
You really should put it in to bridge mode. Here's how;
http://customer.comcast.com/help-and-support/internet/wireless-gateway-enable-disable-bridge-mode