Answer
$\dfrac{5a+1}{(a+1)(a+1)(a-1)}$
Work Step by Step
Factoring the given expression, $
\dfrac{2}{a^2+2a+1}+\dfrac{3}{a^2-1}
,$ results to
\begin{array}{l}\require{cancel}
\dfrac{2}{(a+1)(a+1)}+\dfrac{3}{(a+1)(a-1)}
.\end{array}
Using the $LCD=
(a+1)(a+1)(a-1)
,$ the expression, $
\dfrac{2}{(a+1)(a+1)}+\dfrac{3}{(a+1)(a-1)}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(a-1)(2)+(a+1)(3)}{(a+1)(a+1)(a-1)}
\\\\=
\dfrac{2a-2+3a+3}{(a+1)(a+1)(a-1)}
\\\\=
\dfrac{5a+1}{(a+1)(a+1)(a-1)}
.\end{array}
