The dollar sign, $, must be a misprint. Replace it with a round bracket, ). The question can be rewritten and simplified as follows:
{(x²+3ax) / (3a-x)}·(x²-4ax+3a²) = {x(x+3a) / (3a-x)}·{(x-3a)(x-a)} =
{-x(x+3a) / (x-3a)}·{(x-3a)(x-a)} = -x(x+3a)(x-a) (= -x³-2ax²+3ax)
Answer: -x(x+3a)(x-a)