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Using polynomial division,
(2x - x^3 - 1) / (x - 1) = -x^2-x+1
Plugging in x=1 from the point (1,2)
(2x - x^3 - 1) / (x - 1) = -1
Therefore the slope of the tangent line is -1. Since all lines have the format y=mx+b where m is the slope, we now have
y=-x+b
using the point (1,2) again
2=-1+b
b=3
so the equation of the tangent line is
y=-x+3
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