Derivatives and tangent to the line of a curve

Derivatives and tangent to the line of a curve

Find the equations of all tangent lines to the curve y=x/(x+1) that
intersect the point (1,2). Note that the point (1,2) does not lie on the
curve. Please simplify your final answer as much as possible.
This is what I have done so far. I don't know if it is correct.
1/(x+1)= -x-2/(x-1) [cross-multiplied] to get, x-1=-x^2 -3x -2
I made it equal to zero to get a quadratic equation of x^2 + 4x + 1 = 0 to
solve for x I got x = -2 +- root 3
I dont know what to do next.