#### Answer

$\frac{n}{(n+1)}$

#### Work Step by Step

We factor the expression in the numerator by taking out $n$ as the common factor. Since the denominator consists of a trinomial, we use the rules of factoring trinomials in order to factor it. Then, we cancel out the resultant common factors in the numerator and the denominator:
$\frac{n^{2}+2n}{n^{2}+3n+2}$
=$\frac{n(n+2)}{n^{2}+1n+2n+2}$
=$\frac{n(n+2)}{n(n+1)+2(n+1)}$
=$\frac{n(n+2)}{(n+1)(n+2)}$
=$\frac{n}{(n+1)}$