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 to obtain:
$=\dfrac{2(3+i)}{(3-i)(3+i)}
\\=\dfrac{6+2i}{(3-i)(3+i)}$
Use 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 fact that $i^2=-1$ to obtain:
$=\dfrac{6+2i}{9-(-1)}
\\=\dfrac{6+2i}{9+1}
\\=\dfrac{6+2i}{10}
\\=\dfrac{6}{10} + \dfrac{2}{10}i
\\=\dfrac{3}{5} + \dfrac{1}{5}i$
