Lay both rugs down on the floor with the backing side up. The rugs should be placed in the position in which they will be connected.
Using a utility knife or scissors, trim away any pieces of rug backing that are loose. Be careful not to shred the backing. Place the carpet pieces together, making sure that all of the rug fibers are pointing towards the floor.
Using a hot glue gun, run a zigzag line of hot glue along the edges of the rug that are being joined. Working with a small area at a time, smooth out the hot glue with a flat stick along the seam of both of the rugs. Complete this for the entire length of rug.
Starting back at the beginning, press rug tape into place along the seam that has just been glued. Again, working with small areas at a time, use an iron on the tape to secure it in place. The iron should be at its hottest setting. This will further create a strong bond. When the entire length is taped and ironed, let it cool before turning the rug over.
Using a small hand brush, brush the fibers along the seam, blending them together until the joint can no longer be seen. Trim any rug fibers that are loose. Place the rug in the desired location.