simplifying equations I have been trying to study analysis of algorithms with mathematical induction yet I found my algebra skills are very poor. So now I began restuddiing algebra (factoring, destributive property, simplifying, expanding) so I can handle mathematical equations better. But no matter what I do, I can't seem to explain how the following equation work.
$$
\frac{n(n+1)}{2}+(n+1) = \frac{(n+1)(n+2)}{2}
$$
I think
$$
\frac{n(n+1)}{2}+(n+1)
$$
have been simplified to
$$
\frac{(n+1)(n+2)}{2}
$$
I have a feeling I am thinking something stupid, but I really don't understand how the right side of the equation have been simplified.


*

*Can anyone explain how the formula got simplified?

*What part of algebra should I study to understand equations like this?


Note that both expressions have the common factor $(n+1)$, which we can factor out.  Hence we write $$\frac{n(n+1)}{2}+(n+1)=(n+1)\left[\frac{n}{2}+1\right]=(n+1)\left[\frac{n}{2}+\frac{2}{2}\right]=(n+1)\frac{n+2}{2}=\\=\frac{(n+1)(n+2)}{2}$$
