I am not sure if I am doing this right. Solve for K.

a/b=b/a+1/k
(bak) a/b=(bak)b/a+1/k(bak)
a^2k=b^2k+ba
a^2k-b^2k=ba
k(a^2-b^2)=ab
k=ab/a^2-b^2