The sum of possible value of $ x $ for $ \tan ^{-1}(x+1)+ $ $ \cot ^{-1}\left(\frac{1}{x-1}\right)=\tan ^{-1}\left(\frac{8}{31}\right) $ is [JEE Main 2021, 17 Mar (Shift 1)]

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The sum of possible value of \( x \) for \( \tan ^{-1}(x+1)+ \) \( \cot ^{-1}\left(\frac{1}{x-1}\right)=\tan ^{-1}\left(…

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