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