Turn off the water at the main shut-off valve in your home.
Mark the pipe 6 inches on both sides of the problem area using a black felt tip pen.
Place a tubing cutter around the pipe, tightening the blade onto one of the marks. Rotate the cutter once, before tightening it again. Rotate a second time. Repeat until the pipe is cut through. Follow the same steps at the second mark on the pipe, and remove the piece.
Measure the distance between the two cuts, and cut a new piece of pipe to the same length.
Sand the two cut ends of the existing pipe using emery cloth. Also, sand the ends of the new piece of pipe and the insides of two straight couplings.
Apply a thin layer of soldering paste (flux) to all sanded areas with a small brush.
Push the couplings onto the ends of the existing pipe. Then push the new pipe into the other ends of the couplings.
Uncoil 8 inches of solder from its spool. Bend the last 2 inches 90 degrees.
Heat one of the couplings with the propane torch by moving the flame from side to side. When the flux sizzles, remove the flame. Touch the tip of the solder to one of the coupling seams (between the coupling and pipe). If it melts, apply 3/4-inch of solder to the seam. Solder the coupling's other seam in the same way. Carefully remove excess solder with a rag. Follow this process to solder the other coupling.
Turn the water back on at the main shut-off valve after the couplings have cooled down.