#### Answer

$a+5$

#### Work Step by Step

Adding the numerators and copying the denominator, the given expression, $
\dfrac{a^2}{a-4}+\dfrac{a-20}{a-4}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{a^2+a-20}{a-4}
\\\\=
\dfrac{(a+5)(a-4)}{a-4}
\\\\=
\dfrac{(a+5)(\cancel{a-4})}{\cancel{a-4}}
\\\\=
a+5
.\end{array}