Final answer:
The question involves performing partial fraction decomposition on the algebraic expression (-2x³ +x²+x) / ((x²+3)²). This process decomposes a complex rational expression into simpler fractions that can be easier to integrate or manipulate.
Step-by-step explanation:
The subject of this question is partial fraction decomposition in mathematics, specifically within the context of college-level algebra or calculus. While the provided excerpts reference various equations and their solutions, they do not directly inform the process of deriving the partial fraction decomposition of the given function (-2x³ +x²+x) / ((x²+3)²). To perform partial fraction decomposition, one typically breaks down a complex rational expression into a sum of simpler fractions. However, to accurately determine the partial fractions of the provided expression, we'd need to consider the explicit forms that are compatible with the denominator's structure, which in this instance is a squared binomial. This process can involve setting up an equation with undetermined coefficients that correspond to each term of the denominator when assumed to be factored into linear or irreducible quadratic factors.