\begin{align*} \text{Numerator = } & E[X^3] - 3 \mu E[X^2] + 2\mu^3\\ & = \int_{-1}^1 x^3 \cdot \frac{3}{4} \cdot (1-x^2) dx - 3 E[X^2] \cdot 0 + 0^3 \\ & = \int_{-1}^1 \cdot \frac{3}{4} \cdot (x^3-x^5) dx\\ & = \frac{3}{4} \cdot (x^4/4-x^6/6) \big |_{-1}^1\\ & = 0 \end{align*}