Answer :
Use long division to find the quotient:
[tex]\frac{x^3-x-23}{x+1}[/tex]The procedure of the long division is shown:
As we can see, the quotient is x²-x, with a remainder of -23 when the divisor is x+1.
Therefore, we can rewrite the rational expression as:
[tex]\frac{x^3-x-23}{x+1}=x^2-x-\frac{23}{x+1}[/tex]Where:
[tex]\begin{gathered} q(x)=x^2-x \\ b(x)=x+1 \\ r(x)=-23 \end{gathered}[/tex]Therefore, the answer is:
[tex]x^2-x-\frac{23}{x+1}[/tex]