Algebra: A Combined Approach (4th Edition)

$\dfrac{2a+2b}{3}\cdot\dfrac{a-b}{a^{2}-b^{2}}=\dfrac{2}{3}$
$\dfrac{2a+2b}{3}\cdot\dfrac{a-b}{a^{2}-b^{2}}$ 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: $...=\dfrac{2(a+b)(a-b)}{3(a-b)(a+b)}=\dfrac{2}{3}$