solving for K

I have tried for a long time to find out how you solve for K in the spearman brown prophecy formula (to find out how many items is required in a test to get a certain reliability) and it is very frustrating not knowing how to do this so if anyone could please help me that would be awesome! (I know the end result just not how to get there).
That is
k rxx
rxx' = ---------

Getting to this

rxx' (1-rxx)
k = ------------
rxx' (1-rxx')

How do you describe this solving process?

Also seen as pxx* = N pxx' / 1+ (N-1) pxx'
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