Originally Posted by

**PaulAdrienMauriceDirac** It's ok, so should it be something like this?

$\displaystyle \displaystyle \begin{align*}\frac{P}{x-1}=\frac{Q(x+1)(x-1)+5x-7}{x-1}=Q(x+1)+\frac{5x-7}{x-1}=Q(x+1)+\frac{5x-5-2}{x-1}=Q(x+1)+\frac{5(x-1)}{x-1}-\frac{2}{x-1}=Q(x+1)+5-\frac{2}{x-1}\end{align*}$

and the remainder is -2? I don't understand this, can you explain me why is remainder -2 and not $\displaystyle 5-\frac{2}{x-1}$? Is it because we divided $\displaystyle P$ by $\displaystyle x-1$ in the left side?