y'=a/(x+a)^2
(x+a)^2>; 0, so you need a≥0, and your first step is correct.
But obviously this is not enough. Because the topic requirement is (-2, +∞), this is a continuous interval.
Therefore, the possibility of discontinuity must be ruled out.
Obviously, the discontinuity of this function is x =-a.
So there is -a≤-2.
a≥2