To repair a broken electrical cord, unplug the appliance and cut the section of damaged cord out. Separate the wires on one side and cut each wire separately so the length of each wire is staggered about an inch-and-a-half away from the other ends. Separate the wires on the other end the same way and stagger them so they'll match up with the lengths on the first end (that is, the longest length on one end is the shortest on the other.) It's preferrable to solder the ends together side-by-side after stripping off a quarter-inch of insulation, but if you don't have a soldering iron, strip a half-inch of insulation off each of the wires and twist matching pairs from the two pieces of cord together. When the repaired cord is straightened, none of the bare wires should touch one another since they are at least an inch apart. Wrap the whole job in electrical tape or use heat-shrink tubing so you don't electrocute yourself.
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