Prove that tan^-1(2x)-tan^-1(3x)=pi/4

tan^-12x+ tan^-13x= pi/4

tan^-1{ (2x + 3x ) / ( 1 - 6x²) } = pi / 4

5x / (1-6x²) = tan^-1pi/4 = 1

5x = 1 - 6x​2

6x²+ 5x - 1 = 0

6x²+ 3x + 2x - 1 = 0

3x ( 2x + 1 ) + ( 2x - 1 ) = 0

(3x + 1) (2x - 1) =0

therefore, x = -1/3 or x = 1/2