Rational Expressions and Equations
Like rowing a boat, riding a bicycle is a situation in which going in one direction — downhill — is easy, but going in the opposite direction — uphill — can be more work. The trip to reach a destination may be quick, but the return trip, whether upstream or uphill, will take longer. Rational equations are used to model situations like these. In this chapter, you will work with rational expressions, solve rational equations, and use them to solve problems in a variety of applications.
Sections
- Simplify Rational Expressions — determining the values for which a rational expression is undefined, evaluating rational expressions, and simplifying them, including expressions with opposite factors.
- Multiply and Divide Rational Expressions — multiplying and dividing rational expressions and multiplying and dividing a rational function.
- Add and Subtract Rational Expressions with a Common Denominator — adding and subtracting rational expressions that share a denominator, then simplifying the result.
- Add and Subtract Rational Expressions with Unlike Denominators — finding the least common denominator, rewriting each expression over it, and adding or subtracting.
- Simplify Complex Rational Expressions — simplifying a complex rational expression by writing it as division and by using the least common denominator.
- Solve Rational Equations — solving rational equations, checking for extraneous solutions, and solving a rational equation for a specified variable.
- Solve Proportion and Similar Figure Applications — solving proportions and applications modeled by proportions and by similar figures.
- Solve Uniform Motion and Work Applications — solving applications involving uniform motion and work using rational equations.
- Use Direct and Inverse Variation — solving direct variation problems, inverse variation problems, and applications of each.
This chapter overview is adapted from Elementary Algebra 2e, Chapter 8 Introduction by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, © OpenStax, licensed under CC BY-NC-SA 4.0. Access the original for free at openstax.org. Changes: condensed the chapter introduction and recast the chapter outline as a section list.