Algebra Help on Inductive Proof?

Question

I am trying to learn inductive proofs for a test tomorrow. I am trying to understand a solution for a problem in a book, but my math is a bit rusty. Can somebody explain how these are all equal? I don't understand how the last equation was found from the first equation.

n(n+1)/2 + (n+1) = n(n+1) + 2(n+1)/2 = (n+1)(n+2)/2

Answer 1

factor the numerator.

  (n^2 + n + 2n + 2)/2
= (n^2 + 3n + 2)/2
= ((n+1)(n+2))/2

Answer 2

First One is,

n(n+1)/2 + (n+1)
( n(n+1)+2(n+1) )/2
( (n+1)(n+2) ) /2

Got it?

that final /2 is common for both.