Simplify: (x−1x+1)2−(x+1x−1)2\left(\frac{x-1}{x+1}\right)^2 - \left(\frac{x+1}{x-1}\right)^2(x+1x−1)2−(x−1x+1)2 (assume x≠±1x \neq \pm 1x=±1).
−8x(x2−1)2⋅(x2−1)\frac{-8x}{(x^2-1)^2} \cdot (x^2-1)(x2−1)2−8x⋅(x2−1)
−8x(x+1)2(x−1)2⋅(x2−1)2\frac{-8x}{(x+1)^2(x-1)^2} \cdot (x^2-1)^2(x+1)2(x−1)2−8x⋅(x2−1)2
−8x(x2+1)(x2−1)2\frac{-8x(x^2+1)}{(x^2-1)^2}(x2−1)2−8x(x2+1)
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