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

1.	Solve : `tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)3x`
Answer» `tan^-1(x-1)+tan^-1x+tan^-1(x+1) = tan^-1(3x)` `=>tan^-1(x-1)+tan^-1x = tan^-1(3x)-tan^-1(x+1)` `=>tan^-1((x-1+x)/(1-x(x-1))) =tan^-1((3x-(x+1))/(1+3x(x+1)))` `=>tan^-1((2x-1)/(1+x-x^2)) =tan^-1((2x-1)/(1+3x+3x^2))` `=>(2x-1)/(1+x-x^2) =(2x-1)/(1+3x+3x^2)` `=>(2x-1)/(1+x-x^2) - (2x-1)/(1+3x+3x^2) = 0` `=>(2x-1)(1/(1+x-x^2) - 1/(1+3x+3x^2) )= 0` `=>(2x-1)((1+3x+3x^2-1-x+x^2)/((1+x-x^2)(1+3x+3x^2) ))= 0` `=>(2x-1)((4x^2+2x)/((1+x-x^2)(1+3x+3x^2) ))= 0` `=>2x(2x-1)(2x+1)= 0` `:. x = 0 and x = +-1/2`

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

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