Answer
$\displaystyle \frac{4(x+y)}{3(x-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:
$x^{2}+2xy+y^{2}=(x+y)^{2}$
$x^{2}-2xy+y^{2}=(x-y)^{2}$
$4x-4y=4(x-y)$
$3x+3y=3(x+y)$
Rewrite the problem:
$=\displaystyle \frac{(x+y)^{2}}{(x-y)^{2}}\cdot\frac{4(x-y)}{3(x+y)} \qquad$... divide out the common factors
$=\displaystyle \frac{(x+y)}{(x-y)}\cdot\frac{4\cdot 1}{3\cdot 1}$
= $\displaystyle \frac{4(x+y)}{3(x-y)} $
