First, set up the division problem, that is,
Now, since
[tex]x^3[/tex]
divided by x is
[tex]x^2[/tex]
we have
or equivalently
Since the remainder is -x-9 and its degree is less than 2 (which is the degree of the divisor), then we have that
so, the answer is:
[tex]\frac{x^3-9}{x^2+1}=x-\frac{x+9}{x^2+1}[/tex]
