Simplifying $x^2 + x$ I am currently trying to find a pattern in $x^2+x.$
I am finding that there is a set of multiplicands that show up whenever I lay down numbers $1$ to $10$ in this formula. Make note, I am calculating how much you multiply for example $2^2-2$ to get to $3^2-3$. 
These multiplicands are 
$3$ for $2$, $2$ for $3$, $1 \frac{2}{3}$ for $4$, $1.5$ for $5$, $1.4$ for $6$, $1\frac{1}{3}$ for $7$, and so on. 
I tried to see if there was a logarithmic or exponential connection between these, or something that could at least predict an outcome, and I failed.
I am wondering if there is a certain more simple way to simplify or describe this behavior, or this is a stupid questions like I think it is. Thank you!

It's not a stupid question but it isn't a hard one either.
You can see the pattern much more clearly if you use fractions rather than "mixed numbers":
$$
\frac{3}{1},
\frac{4}{2},
\frac{5}{3},
\frac{6}{4}, \ldots
$$
A little algebra will prove the pattern continues:
You want to find the unknown number $?$ such that
$$
(n^2+n) \times ? = (n+1)^2 + (n+1)
$$
so
$$
? = \frac{(n+1)^2 + (n+1)}{n^2+n} .
$$
Can you finish? Factor the numerator and denominator and see what cancels.
