Answer
$2-i$
Work Step by Step
Multiplying the denominator by $i$, the given expression, $
\dfrac{6i+3}{3i}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{6i+3}{3i}\cdot\dfrac{i}{i}
\\\\=
\dfrac{6i(i)+3(i)}{3i(i)}
\\\\=
\dfrac{6i^2+3i}{3i^2}
\\\\=
\dfrac{6(-1)+3i}{3(-1)}
\\\\=
\dfrac{-6+3i}{-3}
\\\\=
\dfrac{-3(2-i)}{-3}
\\\\=
\dfrac{\cancel{-3}(2-i)}{\cancel{-3}}
\\\\=
2-i
.\end{array}
