Hello everybody, thanks for reading....

I've got this question that I don't seem to be able to solve on my own :-\

R is a ring. x is an nilpotent (?) element in it - meaning that there exists some n in N such that x^n = 0 (and x is not 0 of course).

There were some questions posed, and I got stuck on the last one:

prove that the element (x+u), where u is comutative with x (meaning xu=ux), is reversible (?) (meaning, that there exists an element r in R such that r*(x+u) = (x+u)*r = 1).

I try all the tricks up my sleeve and still am stuck.

a question before I've proved (1+x) is reversible, noticing that:

(1+x)(1-x+x^2-....+x^n-1) = 1 (since x^n is 0)... but this question seems much harder.

Thank you very much for reading/responding!