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If your iPad backup filled up your HDD then the prudent thing would be to get a new HD for your machine. It's pretty easy in most Macs -- if you go to fix.com they have step by step guides for most machines. You may need to buy a torx 8 or 6 driver but that is the most difficult part.

If you want to just put your iTunes library on your external you can. Just go to iTunes preferences and then advanced.
 
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