Answer
$-a-7b+\dfrac{7}{12}$
Work Step by Step
Using the Distributive Property and then combining like terms, the given expression, $
\dfrac{1}{2}(4a-6b)-\dfrac{1}{3}(9a+12b-1)+\dfrac{1}{4}
,$ simplifies to
\begin{array}{l}\require{cancel}
2a-3b-3a-4b+\dfrac{1}{3}+\dfrac{1}{4}
\\\\=
(2a-3a)+(-3b-4b)+\left(\dfrac{1}{3}+\dfrac{1}{4}\right)
\\\\=
(2a-3a)+(-3b-4b)+\left(\dfrac{4}{12}+\dfrac{3}{12}\right)
\\\\=
-a-7b+\dfrac{7}{12}
.\end{array}
