Answer
$\frac{(a+b)^2}{(b-a)}$.
Work Step by Step
The given expression is
$\Rightarrow \frac{a^3+b^3}{ac-ad-bc+bd}\div \frac{ab-a^2-b^2}{ac-ad+bc-bd}$
Invert the divisor and multiply.
$\Rightarrow \frac{a^3+b^3}{ac-ad-bc+bd}\cdot \frac{ac-ad+bc-bd}{ab-a^2-b^2}$
Factor each numerator and denominator as shown below.
$\Rightarrow a^3+b^3$
Use the formula $A^3+B^3=(A+B)(A^2-AB+B^2)$.
$\Rightarrow (a+b)(a^2-ab+b^2)$
$\Rightarrow ac-ad-bc+bd$
Group terms.
$\Rightarrow (ac-ad)+(-bc+bd)$
Factor each group.
$\Rightarrow a(c-d)-b(c-d)$
Factor out $(c-d)$.
$\Rightarrow (c-d)(a-b)$
$\Rightarrow ac-ad+bc-bd$
Group terms.
$\Rightarrow (ac-ad)+(bc-bd)$
Factor each group.
$\Rightarrow a(c-d)+b(c-d)$
Factor out $(c-d)$.
$\Rightarrow (c-d)(a+b)$
$\Rightarrow ab-a^2-b^2$
Factor out $-1$ from each term.
$\Rightarrow -1(a^2-ab+b^2)$
Substitute all factors into the given expression.
$\Rightarrow \frac{(a+b)(a^2-ab+b^2)}{(c-d)(a-b)}\cdot \frac{(c-d)(a+b)}{-1(a^2-ab+b^2)}$
Cancel common terms.
$\Rightarrow \frac{(a+b)}{(a-b)}\cdot \frac{(a+b)}{-1}$
Simplify.
$\Rightarrow \frac{(a+b)^2}{(b-a)}$.
