Answer
$\dfrac{3}{a+5}$
Work Step by Step
Factoring the expressions and then cancelling the common factors between the numerator and the denominator, the given expression, $
\dfrac{3a^2-3}{a^3+5a^2-a-5}
$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{3(a^2-1)}{(a^3+5a^2)-(a+5)}
\\\\=
\dfrac{3(a^2-1)}{a^2(a+5)-(a+5)}
\\\\=
\dfrac{3(a^2-1)}{(a+5)(a^2-1)}
\\\\=
\dfrac{3(\cancel{a^2-1})}{(a+5)(\cancel{a^2-1})}
\\\\=
\dfrac{3}{a+5}
.\end{array}
