Solve : `tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)3x`

Answer

`x=0, frac{1}{2},-frac{1}{2}`

Explanation

ATQ, It is given

\begin{aligned}
&\tan ^{-1}(x-1)+\tan ^{-1} x+\tan ^{-1}(x+1)=\tan ^{-1} 3 x\\ \\
&\tan ^{-1}(x-1)+\tan ^{-1}(x+1)\\
&=\tan ^{-1} 3 x-\tan ^{-1} x\\
&\text { or } \tan ^{-1}\left(\frac{2 x}{2-x^{2}}\right)=\tan ^{-1}\left(\frac{2 x}{1+3 x^{2}}\right)\\
&\text { or } \frac{2 x}{2-x^{2}}=\frac{2 x}{1+3 x^{2}}\\
&\text { or } 2 x\left(1+3 x^{2}-2+x^{2}\right)=0\\
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