Answer
$\dfrac{3-i}{5}$
Work Step by Step
Multiplying by the conjugate of the denominator, the expression $
\dfrac{2}{3+i}
$ simplifies to
\begin{array}{l}
\dfrac{2}{3+i}
\cdot
\dfrac{3-i}{3-i}
\\\\=
\dfrac{6-2i}{9-i^2}
\\\\=
\dfrac{6-2i}{9-(-1)}
\\\\=
\dfrac{6-2i}{10}
\\\\=
\dfrac{3-i}{5}
.\end{array}
