This is a step during a mathematical induction inside a textbook example I don't get, why is
$1-\frac{1}{(n+1)}+\frac{1}{(n+1)(n+2)} = 1-\frac{(n+2)-1}{(n+1)(n+2)}$
Also, if anyone has some good online resources to practice this sort of stuff, I'd be eternally grateful!
Edit:
I added a picture of the textbook page. Hopefully that makes it a bit clearer, what I posted earlier was part of a mathematical induction, which may have caused some confusion.
Because
$$1-{1\over n+1} + {1\over (n+1)(n+2)} \\ = 1-{n+2\over (n+1)(n+2)} + {1\over (n+1)(n+2)} \\ = 1-\left({n+2\over (n+1)(n+2)} - {1\over (n+1)(n+2)}\right) \\ = 1-\left({(n+2) - 1\over (n+1)(n+2)} \right) \\ = 1-{(n+2) - 1\over (n+1)(n+2)} \\ $$