3. [-/1 Points] DETAILS MY NOTES TGEIALG6 5.8.073. Perform the division. (Simplify your answer completely.) \( \frac{x^{3}+1}{x+1} \) Ta

To perform the division \( \frac{x^{3}+1}{x+1} \), we can factor the numerator first. The expression \( x^{3}+1 \) can be factored using the sum of cubes formula \( a^3 + b^3 = (a + b)(a^2 - ab + b^2) \). Here, \( a = x \) and \( b = 1 \), so we have: \[ x^{3}+1 = (x+1)(x^2 - x + 1). \] Now, substitute this back into the division: \[ \frac{(x+1)(x^2 - x + 1)}{x+1}. \] Since \( x + 1 \) in the numerator and denominator are the same and \( x \neq -1 \), we can cancel them out, leading to the simplified result: \[ x^2 - x + 1. \] So, the answer is \( x^2 - x + 1 \!).