In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. (3x+16)/(x + 1) (x − 2)²

A rational expression is a fraction where both the numerator and the denominator are polynomials. Understanding rational expressions is crucial for performing operations such as addition, subtraction, multiplication, and division, as well as for decomposing them into simpler components, which is the focus of this question.

Partial fraction decomposition is a technique used to express a rational function as a sum of simpler fractions. This method is particularly useful for integrating rational functions or simplifying complex expressions. The decomposition involves breaking down the rational expression based on the factors of the denominator, which can include linear and irreducible quadratic factors.

The degree of a polynomial is the highest power of the variable in the expression. In partial fraction decomposition, understanding the degree of the polynomial in the denominator helps determine the form of the decomposition. Additionally, factorization of the denominator into linear and quadratic factors is essential for setting up the correct structure of the partial fractions.