Find the value of `tan^(-1)((x-2)/(x-1))+tan^(-1)((x+2)/(x+1))=pi/4`

Explanation

To solve the equation \( \tan^{-1}\left(\frac{x-2}{x-1}\right) + \tan^{-1}\left(\frac{x+2}{x+1}\right) = \frac{\pi}{4} \), we can use the formula for the sum of inverse tangents:

\[ \tan^{-1}(a) + \tan^{-1}(b) = \tan^{-1}\left(\frac{a+b}{1-ab}\right) \]

provided that \( ab < 1 \).

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