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Question: How to obtain this representation?

Question:How to obtain this representation?

SandorSzabo 607 Maple 2015
convert simplify
December 10 2015
0

It is given 

   xn (n x - n - x) / (x-1)2 + x / (x-1)2  , n is a (symbolic) positive integer.

I want to transform it into

n xn+1 / (x-1) - x (xn-1) / (x-1)2. 

How is it possible?

I tried the  simplify, convert (parfrac), collect, combine, expand,  with/without assuming.

Thanks in advance.
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