Answer
$\dfrac{3}{16}x^2+\dfrac{11}{4}x-4$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the Distributive Property, the given expression, $
\left( \dfrac{1}{4}x+4 \right)\left( \dfrac{3}{4}x-1 \right)
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{1}{4}x\left( \dfrac{3}{4}x \right)+\dfrac{1}{4}x(-1)+4\left( \dfrac{3}{4}x \right)+4(-1)
\\\\=
\dfrac{3}{16}x^2-\dfrac{1}{4}x+\dfrac{12}{4}x-4
\\\\=
\dfrac{3}{16}x^2+\dfrac{11}{4}x-4
.\end{array}
