The system of equations left at x = 0 is

A + B = D

ikA - ikB = -aD (for the derivatives)

And he wrote that

D = (2k)/(k + ia)

and

B = (k - ia)/(k + ia)

He said we can "invert" the original equations to get those. After many attempts, I can't figure it out. Can someone please guide me along before I pull all of my hair out?