## Elementary Algebra

$\frac{(x-y)}{(x+2y)}$
Since the numerator consists of a trinomial, we use the rules of factoring trinomials in order to factor it. For the factoring of the denominator, we use the rule $a^{2}-b^{2}=(a+b)(a-b)$. Then, we cancel out the resultant common factors in the numerator and the denominator: $\frac{x^{2}-3xy+2y^{2}}{x^{2}-4y^{2}}$ =$\frac{x^{2}-1xy-2xy+2y^{2}}{x^{2}-(2y)^{2}}$ =$\frac{x(x-y)-2y(x-y)}{(x+2y)(x-2y)}$ =$\frac{(x-y)(x-2y)}{(x+2y)(x-2y)}$ =$\frac{(x-y)}{(x+2y)}$