I guess the equation was meant to be x+1=2/(x-1).
Multiply both sides by x-1: x²-1=2, x²-1-2=0, x²-3=0=(x-√3)(x+√3).
So x+√3=0 is a solution, therefore the value of x+√3 is zero.
(If x-√3=0 is taken to be the other solution, then x=√3 and the value of x+√3 would be 2√3.)