Answer
$\frac{1+2x^3-2x}{4}$
Work Step by Step
Start with cancelling the common factor $4(x^2-1)^3$, we have:
$\frac{4(x^2-1)^3+8x(x^2-1)^4}{16(x^2-1)^3}=\frac{1+2x(x^2-1)}{4}=\frac{1+2x^3-2x}{4}$
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