Answer
$$y = -x+1$$
Work Step by Step
Let the equation of the tangent be $$y=mx+c$$
We know that the slope $m =\frac{dy}{dx}|_{x=-1}$ at x=-1
Or $m=\frac{1}{2+x}-\frac{2}{(2+x)^2}|_{x=-1} = -1$
Therefore, $y=-x+C$
But the tangent must pass through the given point. So, (-1, 2) is a point on the tangent. Therefore, $2 = -(-1)+C$ or $C=1$.
Thus $$y = -x+1$$ is the tangent of the given function at the given point/