Likewise to you, I slipped on the same mistake: Equation 4.12 represents the expression for the Zero, not for the Pole. In order to obtain equation 4.23 you should have to agebraically develop equation 4.11 and then obtain the expression for the global denominator, since in this equation the result is presented as a sum of partial equations that, if expanded, would have different denominators. By the way, you omit part of the text (for example equation 4.22) but nevertheless, surely somewhere the author must have mentioned some criterion of stability analysis (eg Routh-Hurwitz), which should have generated the equations 4.24 for example.