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Good question. It is not possible to cancel the m's. Doing so is a common type of algebra mistake. "cancelling" really means dividing every term on the top by the bottom, so if you tried cancelling the m's, you would end up with $\dfrac{F_c}{m} - g$. Notice that, which the m's did cancel from the second term, the 'm' is still hanging around under the Fc term.