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

Answer

`x = pm sqrt{7/2}
`

Explanation

ATQ,
$$ \tan ^{-1}\left(\frac{x-2}{x-1}\right)+\tan ^{-1}\left(\frac{x+2}{x+1}\right)=\frac{\pi}{4} $$
Operating on LHS only, then we get:
$$
\begin{aligned}
&\tan ^{-1}\left(\frac{x-2}{x-1}\right)+\tan ^{-1}\left(\frac{x+2}{x+1}\right) \tan ^{-1}\left(\frac{x-2}{x-1}\right)+\tan ^{-1}\left(\frac{x+2}{x+1}\right) \\ \\
...