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If f(x)=loge((1-x)/(1+x)); prove that f(...

If `f(x)=log_e((1-x)/(1+x));` prove that `f(a)+f(b)=f((a+b)/(1+a b))`

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The correct Answer is:
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`f(x)log""(1-x)/(1+x)`
`Now, L.H.S. =f(a)+f(b)`
`log""(1-a)/(1+a)+log""(1-b)/(1+b)`
`=log[(1-a)/(1+a).(1-b)/(1+b)]`
`=log[(1+ab-(a+b))/(1+ab+(a+b))]`
`=log[(1-(a+b)/(a+ab))/(1+(a+b)/(1+ab))]`
`=f((a+b)/(a+ab))=R.H.S.`
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