How to simplify this example from induction n(n+1)/2 + (n+1)

Question

I am trying to figure out the steps here, not even sure what to really google as the topic to understand it.

My thoughts are

1. Multiply it out to get $\dfrac{n^2}{2} + \dfrac{n}{2} + (n + 1)$
2. You then times by $2$ to get ${n^2} + {3n} + {2}$

But then I am stuck. Can someone please walk through the steps that were done to reduce this.

Example taken from how to read and do proofs by Daniel Slow. I know this may be a stupid question just trying to really understand it.

Answer 1

$$ \begin{split} \dfrac{n(n+1)}{2} + (n+1)&= \dfrac{n(n+1)}{2} + \dfrac{2(n+1)}{2} \\ &= \dfrac{n(n+1) + 2(n+1)}{2} \\ &= \dfrac{(n+1)(n+2)}{2} \end{split} $$

Answer 2

First , the common term $\ n+1\ $ is factored out, then two fractions are added by bringing them to the same denominator.