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 above 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}
