What are the stepps to this shortcut?

Question

I looked at an answer for a question and I don't know how they came to this conclusion.

$(k+1)!-1 + (k+1)!(k+1) = (k+2)! - 1$

What are the stepps behind it?

Answer 1

Hint: $(k+1)! + (k+1)!(k+1) = (k+1)! (1 + (k+1)) = (k+2)!.$