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How to change a bicycle brake cable
Snip the crimped end off of the inner cable.
Find the end of the brake cable that sticks out of the retention clamp on the braking mechanism. This is the wheel-end of the cable, as opposed to the end that attaches to the lever.
Use a pair of wire cutters to snip off the crimp on the end. It'll be easier to slide the old cable out of its housing if you snip off the crimped end.