Answer
$\displaystyle \frac{x+2y}{2x+y} $
Work Step by Step
Step by step multiplication of rational expressions:
1. Factor completely what you can
2. Reduce (divide) numerators and denominators by common factors.
3. Multiply the remaining factors in the numerators and
multiply the remaining factors in the denominators. $(\displaystyle \frac{P}{Q}\cdot\frac{R}{S}=\frac{PR}{QS})$
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Factor what we can:
$x^{2}-y^{2}=(x+y)(x-y)$
$ 2x^{2}-xy-y^{2}=\qquad$... factors of $ac$ whose sum is $b$ ... $-2$ and $+1$
$=2x^{2}-2xy+xy-y^{2}$
$=2x(x-y)+y(x-y)$
$=(x-y)(2x+y)$
Rewrite the problem:
$=\displaystyle \frac{(x+y)(x-y)}{(x+y)}\cdot\frac{x+2y}{(x-y)(2x+y)} \qquad$... divide out the common factors
$=\displaystyle \frac{1\cdot 1}{1}\cdot\frac{x+2y}{1\cdot(2x+y)} $
= $\displaystyle \frac{x+2y}{2x+y} $
