Answer:
[tex]x+2[/tex]
Step-by-step explanation:
For this division we can first use factoring of the numerator, then eliminate the common factors.
[tex]\frac{x^{3} +2x^{2} +x+2}{x^{2}+1 }[/tex]
Factoring the numerator by the term grouping method
[tex]\frac{x^{2} (x+2)+(x+2) }{x^{2} +1}[/tex]
[tex]\frac{(x^{2} +1)(x+2)}{x^{2} +1}[/tex]
removed terms
[tex](x+2)[/tex]
