## Elementary Algebra

$\frac{n}{(n+1)}$
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: $\frac{n^{2}+2n}{n^{2}+3n+2}$ =$\frac{n(n+2)}{n^{2}+1n+2n+2}$ =$\frac{n(n+2)}{n(n+1)+2(n+1)}$ =$\frac{n(n+2)}{(n+1)(n+2)}$ =$\frac{n}{(n+1)}$