If $f(x)=\log \frac{1+x}{1-x}$, then $f(a)+f(b)$ is equal to

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Professor PC Thomas Classes · Answer

$f(a)+f(b) = \log\frac{1+a}{1-a} + \log\frac{1+b}{1-b} = \log\frac{1+a+b+ab}{1-(a+b)+ab} = f\left(\frac{a+b}{1+ab}\right)$.