Answer
$C$
Work Step by Step
Factor each polynomial completely:
$\dfrac{x}{(x - 3)(x + 1)} \cdot \dfrac{2(x - 3)}{(x - 3)(x - 1)}$
Cancel the common factors in the numerator and denominator:
$\require{cancel}
=\dfrac{x}{\cancel{(x - 3)}(x + 1)} \cdot \dfrac{2\cancel{(x - 3)}}{(x - 3)(x - 1)}$
$=\dfrac{2x}{(x + 1)(x - 1)(x - 3)}$
This answer corresponds to option $C$.
