Question: Simplification equation not commutative

Dear all

My goal us to show that equation (11) is exactly (q^n-1)/(q-1)*y^(n-1),   a  simplification must be introduced and so that we obtain the necessary (q^n-1)/(q-1)*y^(n-1). 
Note that the operators are not commutative.

 

Question.mw

Than you for your help

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