The rate law depends on only A because it is the reactant in the rate-determining step.
The rate law is a representation of the rate of reaction. The fast reaction is E+B ------> A+ D. The slow reaction is A + A ----->C + E. The overall reaction is A + B ------> C + D.
We know that the rate law depends only on the the slow reaction hence the rate law depends on only A because it is the reactant in the rate-determining step.
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