#### Answer

$\dfrac{\dfrac{ax+ab}{x^{2}-b^{2}}}{\dfrac{x+b}{x-b}}=\dfrac{a}{x+b}$

#### Work Step by Step

$\dfrac{\dfrac{ax+ab}{x^{2}-b^{2}}}{\dfrac{x+b}{x-b}}$
Evaluate the division:
$\dfrac{\dfrac{ax+ab}{x^{2}-b^{2}}}{\dfrac{x+b}{x-b}}=\dfrac{ax+ab}{x^{2}-b^{2}}\div\dfrac{x+b}{x-b}=\dfrac{(ax+ab)(x-b)}{(x^{2}-b^{2})(x+b)}=...$
Take out common factor $a$ from the first parentheses in the numerator and factor the first parentheses in the denominator and then simplify:
$...=\dfrac{a(x+b)(x-b)}{(x-b)(x+b)(x+b)}=\dfrac{a}{x+b}$