Answer
$\dfrac{3}{5} - \dfrac{1}{5}i$
Work Step by Step
Rationalize the denominator by multiplying the conjugate of the denominator, which is $3-i$, to both the numerator and the denominator:
$=\dfrac{2(3-i)}{(3+i)(3-i)}$
Simplify using the rule $(a+b)(a-b) = a^2-b^2$ to obtain:
$=\dfrac{6-2i}{3^2-i^2}
\\=\dfrac{6-2i}{9-i^2}$
Use the rule $i^2=-1$ to obtain:
$=\dfrac{6-2i}{9-(-1)}
\\=\dfrac{6-2i}{9+1}
\\=\dfrac{6-2i}{10}
\\=\dfrac{6}{10} - \dfrac{2}{10}i
\\=\dfrac{3}{5} - \dfrac{1}{5}i$
