Answer: It's not impossible to divide a fuchsia, but it is difficult. If you want to increase your stock of fuchsias, why not take some tip cuttings and root them in moistened potting soil? Pinching back the tips of the stems will result in a full plant with lots of flowering stems - instead of pinching the tips of the stems, you can cut a 4-6" length, strip the lower leaves, dip the cut end in rooting hormone and place it in a container of moist potting soil. Keep the soil moist and the cutting should root in a few weeks.
Best wishes with your fuchsia!
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