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If tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/...

If `tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=pi/4`, then find the value of `x`.

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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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