Answer
$=\displaystyle \frac{18i-6}{10}$
Work Step by Step
$\displaystyle \frac{6i}{3-i}\qquad$ ...multiply both numerator and denominator by $3-i$
$=\displaystyle \frac{6i(3+i)}{(3-i)(3+i)}\qquad$ ...use the FOIL method.
$=\displaystyle \frac{18i+6i^{2}}{9+3i-3i-i^{2}}\qquad$ ...simplify. ($i^{2}=-1$)
$=\displaystyle \frac{18i-6}{9+1}\qquad$ ...simplify.
$=\displaystyle \frac{18i-6}{10}$
