$AB\overset {{K_1}} \longleftrightarrow {A^ + } + {B^{ - 1}}$

${K_1} = \frac{{[{A^ + }][{B^ - }]}}{{[AB]}}$

$AB + {B^ - }\overset {{K_2}} \longleftrightarrow AB_2^ - $

${K_2} = \frac{{[AB_2^ - ]}}{{[AB][{B^ - }]}}$

Dividing $K_1$ and $K_2$ we get

$K = \frac{{{K_1}}}{{{K_2}}} = \frac{{[{A^ + }]{{[{B^ - }]}^2}}}{{[AB_2^ - ]}}$

$\therefore \,\frac{{[{A^ + }]}}{{[AB_2^ - ]}} = \frac{K}{{{{[{B^ - }]}^2}}}$