Broken step on staircase
Staple or tack the carpet to the bottom side of the tread above the broken tread, just past where you staple it, cut it with a sharp carpet knife and peal it back, fix the broken tread and then pull the carpet back in place and staple it back into place.  Since all of the stapling and cutting will be on the underside of tread it shouldn't be very noticeable. 

Or hire a carpet guy on craigslist or something to come and pull all of it up and relay it for you after you've fixed it. I assume this would cost about $100.