Answer
$3-i$
Work Step by Step
Multiplying by the conjugate of the denominator, the given expression, $
\dfrac{10}{3+i}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{10}{3+i}\cdot\dfrac{3-i}{3-i}
\\\\=
\dfrac{10(3)+10(-i)}{9-i^2}
\\\\=
\dfrac{30-10i}{9-(-1)}
\\\\=
\dfrac{30-10i}{10}
\\\\=
\dfrac{10(3-i)}{10}
\\\\=
\dfrac{\cancel{10}(3-i)}{\cancel{10}}
\\\\=
3-i
.\end{array}