You can patch a small hole, tear or burn with some techniques that will make the repair virtually invisible. In order to do so, hopefully you have a piece carpet left over from the original install that matches the damaged area . If you don't have a remnant, you can steal a piece from inside a closet or underneath a piece of furniture you never intend to move. (This may sound extreme, but it's a lot cheaper than replacing the entire carpet.)
If you have a “plush”-type carpet with a flat surface and no pattern, we can make a repair that's absolutely invisible. If your carpet has a color pattern, a textured surface design or looped yarn, the match will be determined by the size of the extra piece and size of the damaged area. In some cases the repair may be visible (but you're probably the only one who will notice it).