polynomial division

Find the remainder when x^15 + 1 is divided by x-1.

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     $(x^{15}$ $+1)$    :  $(x-1)$ $=x^{14}+x^{13}+…+x^2+x$$+\large \frac{x+1}{x-1}$

      $\underline{x^{15}-x^{14}}$                                                                     

                 $x^{14}$

                 $\underline{x^{14}-x^{13}}$                                                            $\frac{x+1}{x-1}=1+\frac{2}{x-1}$

                            $x^{13 }$

                                     .... $\underline{x^2-x}$ 

                                                    $x\color{red}+1$ 

  !