MOP Pg. 177

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MOP Pg. 177

Edit:  The mistake (on my part) was that the authors did not claim the first "equation" to actually be an equality.  They claimed that that the RHS led to the LHS as the expression for Player Y's equity when betting with an Ace.

Is it just me or is there an algebraic mistake at the top of page 177?

The authors claim:

(1/(1+q)) -1 + k = (k - q + kq)/ ((k)(1+q))

However, multiplying the LHS by (1+q)/(1+q) where applicable gives:

(1/(1+q)) -1 + k = (k + kq - q) / (1+q)

Why are they including an extra factor of k in the denominator?  I mean, if you use real numbers for the parameters then the second formula gives the correct equality.  It's kind of important because they go on to use the first formula in deriving the number of total kings that we check, but it seems like this formula is wrong. 

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