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I think if you know the overall rate law that was determined experimentally, then the rate law of the slow step will be the same as the reaction rate law. You also might need to use the pre-equilibrium method if the rate law of the slow step has an intermediate.
The slow step of a reaction can also be determined experimentally as the textbook does mention that some techniques such as the stopped-flow technique or spectrometry can be used to measure the rate of fast reactions.
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