Hi,
try to move the problem from angular speed to "linear" speed. The Earth moves with speed Ve, the KBO with speed V, so the relative speed between Earth and KBO is Ve - V.
Now, the "linear" speed can be rewritten as the angular speed times the radius, so we can write the relative speed as the distance between Earth and KBO multiplied by the relative angular speed (Vrel=Ve-V = ω(r-1)[AU]). Here your resoult.
(Note that this is true only in the case opposition or if r>>1)
I apologize for (really) possible English mistakes, I need a bit of training about that.