5. [-/1 Points] DETAILS MY NOTES TGEIALG6 5.8. Perform the division. (Simplify your answer completely.) \[ \frac{y^{3}+y}{y-2} \] \( \square \) SUBMIT ANSWER 6. [-/1 Points] DETAILS MY NOTES TGEIALG6 5.8.0

To perform the division \(\frac{y^{3}+y}{y-2}\), we start by simplifying the numerator, which can be rewritten as \(y(y^2 + 1)\). Then, using polynomial long division or synthetic division, we divide \(y^{3} + y\) by \(y - 2\). The result will include a quotient and a remainder that can be expressed as \(\frac{R}{y-2}\) if applicable. After going through the steps, the answer will help you identify any terms that can further simplify. This process is not just about getting the answer but also about understanding how to work with polynomials! Polynomial long division is similar to regular long division and is a valuable skill in algebra that can help you solve more complex expressions and equations as you progress. Don't forget to check your work at the end, as small errors can lead to significant differences in your final answer!