I am trying to solve an induction problem and got stuck at this part.

$$ 1 - \frac{n+2}{(n+2)!} + \frac{n+1}{(n+2)!} = 1 - \frac{(n+2) - (n+1)}{(n+2)!} $$

Shouldn't it be

$$ 1 - \frac{n+2}{(n+2)!} + \frac{n+1}{(n+2)!} = 1 - \frac{(n+2) + (n+1)}{(n+2)!} $$

How do you get the left expression to the right expression?