1 / 18

Understanding Rational Expressions: Definitions, Simplification, and Operations

This section covers the fundamentals of rational expressions, which are fractional expressions consisting of polynomials in their numerator and denominator. It explains domains, simplification techniques, and operations such as addition, subtraction, multiplication, and division of rational expressions. Key concepts like identifying restrictions, factoring completely, and utilizing the least common denominator (LCD) are emphasized. Additionally, it presents examples to illustrate each operation and the process of rationalizing numerators and denominators.

benita
Télécharger la présentation

Understanding Rational Expressions: Definitions, Simplification, and Operations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 1 - Fundamentals Section 1.4 Rational Expressions 1.4 - Rational Expressions

  2. Definitions • Fractional Expression A quotient of two algebraic expressions is called a fractional expression. • Rational Expression A rational expression is a fractional expression where both the numerator and denominator are polynomials. 1.4 - Rational Expressions

  3. Domain The domain of an algebraic expression is the set of real numbers that the variable is permitted to have. 1.4 - Rational Expressions

  4. Basic Expressions & Their Domains 1.4 - Rational Expressions

  5. Simplifying Rational Expressions To simplify rational expressions we must • Factor the numerator and denominator completely. • State the restrictions or domain. • Reduce the common factors from the numerator and denominator. 1.4 - Rational Expressions

  6. Example 1 • Simplify the following expression. 1.4 - Rational Expressions

  7. Multiplying Rational Expressions To multiply rational expressions we must • Factor the numerator and denominator completely. • State the restrictions or domain. • Multiple factors. • Reduce the common factors from the numerator and denominator. 1.4 - Rational Expressions

  8. Example 2 • Perform the multiplication and simplify. 1.4 - Rational Expressions

  9. Dividing Rational Expressions To divide rational expressions we must • Factor the numerator and denominator completely. • State the restrictions or domain. • Invert the divisor and multiply. • State new restrictions. • Reduce the common factors from the numerator and denominator. 1.4 - Rational Expressions

  10. Example 3 – pg. 42 #33 • Perform the multiplication and simplify 1.4 - Rational Expressions

  11. Adding or Subtracting Rational Expressions To add or subtract rational expressions we must • Factor the numerator and denominator completely. • State the restrictions or domain. • Find the LCD. • Combine fractions using the LCD. • Use the distributive property in the numerator and combine like terms. • If possible, factor the numerator and reduce common terms. 1.4 - Rational Expressions

  12. Example 4 – pg. 42 #48 Perform the addition or subtraction and simplify. 1.4 - Rational Expressions

  13. Compound Fractions • A compound fraction is a fraction in which the numerator, denominator, or both, are themselves fractional expressions. 1.4 - Rational Expressions

  14. Simplifying Compound Fractions To simplify compound expressions we must • Factor the numerator and denominator completely. • State the restrictions or domain. • Find the LCD. • Multiply the numerator and denominator by the LCD to obtain a fraction. • Simplify. • If possible, factor. 1.4 - Rational Expressions

  15. Example 5 – pg. 42 #60 Perform the addition or subtraction and simplify. 1.4 - Rational Expressions

  16. Rationalizing • If a fraction has a numerator (or denominator) in the form then we may rationalize the numerator (or denominator) by multiplyting both the numerator and denominator by the conjugate radical . 1.4 - Rational Expressions

  17. Example 6 – pg. 43 #81 • Rationalize the denominator. 1.4 - Rational Expressions

  18. Example 7 – pg. 43 #87 • Rationalize the numerator. 1.4 - Rational Expressions

More Related