Solve : `tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=pi/4`

Explanation

To solve the equation

\[ \tan^{-1}\left(\frac{x-1}{x-2}\right) + \tan^{-1}\left(\frac{x+1}{x+2}\right) = \frac{\pi}{4}, \]

we can use the formula for the sum of inverse tangents:

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