The common denominator is $(n-1)!k!(n-k)!$. So, we rewrite the left side of the equation:
$$\frac{(n-1)!(n-k)}{k!(n-k)!} + \frac{(n-1)!k}{k!(n-k)!} = \frac{n!}{k!(n-k)!}$$
Now, we can combine the fractions on the left side:
$$\frac{(n-1)!(n-k+k)}{k!(n-k)!} =
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