#### Answer

$\dfrac{x^{2}-y^{2}}{3x^{2}+3xy}\cdot\dfrac{3x^{2}+6x}{3x^{2}-2xy-y^{2}}=\dfrac{x+2}{3x+y}$

#### Work Step by Step

$\dfrac{x^{2}-y^{2}}{3x^{2}+3xy}\cdot\dfrac{3x^{2}+6x}{3x^{2}-2xy-y^{2}}$
Factor both rational expressions completely:
$\dfrac{x^{2}-y^{2}}{3x^{2}+3xy}\cdot\dfrac{3x^{2}+6x}{3x^{2}-2xy-y^{2}}=\dfrac{(x-y)(x+y)}{3x(x+y)}\cdot\dfrac{3x(x+2)}{(x-y)(3x+y)}$
Evaluate the product of the two rational expressions and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression:
$...=\dfrac{3x(x-y)(x+y)(x+2)}{3x(x+y)(x-y)(3x+y)}=\dfrac{x+2}{3x+y}$