Answer
$\dfrac{c+d}{2}$
Work Step by Step
The given expression, $
\dfrac{ac+ad+bc+bd}{a^2-b^2}\cdot\dfrac{a^3-b^3}{2a^2+2ab+2b^2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(ac+ad)+(bc+bd)}{(a+b)(a-b)}\cdot\dfrac{(a-b)(a^2+ab+b^2)}{2(a^2+ab+b^2)}
\\\\=
\dfrac{a(c+d)+b(c+d)}{(a+b)(a-b)}\cdot\dfrac{(a-b)(a^2+ab+b^2)}{2(a^2+ab+b^2)}
\\\\=
\dfrac{(c+d)(a+b)}{(a+b)(a-b)}\cdot\dfrac{(a-b)(a^2+ab+b^2)}{2(a^2+ab+b^2)}
\\\\=
\dfrac{(c+d)(\cancel{a+b})}{(\cancel{a+b})(\cancel{a-b})}\cdot\dfrac{(\cancel{a-b})(\cancel{a^2+ab+b^2})}{2(\cancel{a^2+ab+b^2})}
\\\\=
\dfrac{c+d}{2}
.\end{array}
