#### Answer

$\dfrac{2a+2b}{3}\cdot\dfrac{a-b}{a^{2}-b^{2}}=\dfrac{2}{3}$

#### Work Step by Step

$\dfrac{2a+2b}{3}\cdot\dfrac{a-b}{a^{2}-b^{2}}$
Take out common factor $2$ from the numerator of the first fraction and factor the denominator of the second fraction:
$\dfrac{2a+2b}{3}\cdot\dfrac{a-b}{a^{2}-b^{2}}=\dfrac{2(a+b)}{3}\cdot\dfrac{a-b}{(a-b)(a+b)}=...$
Evaluate the product and simplify by removing the factors that appear both in the numerator and denominator of the resulting expression:
$...=\dfrac{2(a+b)(a-b)}{3(a-b)(a+b)}=\dfrac{2}{3}$