Apply tan to both sides:
tan [tan^-1 (x+1) +tan^-1 (x-1)] = tan(tan^-1 8/31)
[(x+1) + (x-1)] / [1- (x+1)(x-1)] = 8/31
by using tan(a+b) formula.
==> 2x/ (2 - x^2) = 8/31.
==>16 - 8x^2 = 62x
==> 4x^2 + 31x - 8 = 0
==> (4x - 1)(x + 8) = 0.
==> x = 1/4 or -8.