Are Trigonometric Substitutions Needed?

Algebra Level 4

Let \(f(x) = \log \left( \dfrac{1+x}{1-x} \right) \), where \(-1<x<1\). Which of the following choices is equal to \( f \left( \dfrac{3x+x^3}{1+3x^2} \right) - f\left( \dfrac{2x}{1+x^2}\right) \)?

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