Answer
$\dfrac{2a-5}{a-4}$
Work Step by Step
Subtracting the numerators and copying the denominator, the given expression, $
\dfrac{2a^2+15}{a^2-7a+12}-\dfrac{11a}{a^2-7a+12}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2a^2+15-11a}{a^2-7a+12}
\\\\=
\dfrac{2a^2-11a+15}{a^2-7a+12}
\\\\=
\dfrac{(2a-5)(a-3)}{(a-4)(a-3)}
\\\\=
\dfrac{(2a-5)(\cancel{a-3})}{(a-4)(\cancel{a-3})}
\\\\=
\dfrac{2a-5}{a-4}
.\end{array}
