I am asked to prove this given $1 \le m \le n - 1$ (homework question):
$\frac{n!}{(m-1)!(n-m+1)!} + \frac{n!}{m!(n-m)!} = \frac{(n+1)!}{m!(n+1-m)!}$
Which proof technique should I use to solve this? I tried induction but couldn't seem to get anywhere with it. Maybe I am just bad with factorial, should I use induction?