Make The Condition Satisfied

Algebra Level 4

Let \(P(x)=\ln\dfrac{1-x}{1+x}\). For some \(a\) and \(b\) The condition \(P(a)+P(b)=P \left (\dfrac{a+b}{1+ab} \right )\) is satisfied.

Given that \(a\in (f,g)\) and \(b\in (m,n)\). \(f<g\) and \(m<n\).

Find \((g-f)\times(n-m)\)

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