Answer
$\dfrac{9}{a+3}$
Work Step by Step
When adding two fractions with common denominators, we add the numerators and copy the denominator. Therefore, $
\dfrac{4}{a+3}+\dfrac{5}{a+3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{4+5}{a+3}
\\\\=
\dfrac{9}{a+3}
.\end{array}