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.(11x - 10)/(x − 2) (x + 1)

Key Concepts

Rational Expressions

A rational expression is a fraction where both the numerator and the denominator are polynomials. Understanding rational expressions is crucial for performing operations like addition, subtraction, and decomposition. In this context, the expression (11x - 10)/(x - 2)(x + 1) is a rational expression that needs to be decomposed into simpler fractions.

Partial Fraction Decomposition

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 goal is to break down the given rational expression into components that are easier to work with, typically involving linear factors in the denominator.

Linear Factors

Linear factors are expressions of the form (ax + b), where a and b are constants. In the context of partial fraction decomposition, recognizing the linear factors in the denominator is essential for determining the form of the decomposition. For the expression given, the factors (x - 2) and (x + 1) are linear, which influences how the partial fractions will be structured.