1 / 16

223 Reference Chapter

223 Reference Chapter. The quotient of two polynomials is called a Rational Expression.

kacy
Download Presentation

223 Reference Chapter

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. 223 Reference Chapter The quotient of two polynomials is called a Rational Expression. Determining the Domain: Remember, the denominator cannot be zero (that would make the fraction undefined.) So a rational expression would have a domain of all real numbers, with the exception of values that make the denominator zero. Example: Find the domain of each of the following expressions 1. 2. 3. Section R5: Rational Expressions

  2. 223 Reference Chapter The quotient of two polynomials is called a Rational Expression. Determining the Domain: Remember, the denominator cannot be zero (that would make the fraction undefined.) So a rational expression would have a domain of all real numbers, with the exception of values that make the denominator zero. Example: Find the domain of each of the following expressions 1. all real numbers except -4 2. All real numbers except -2, 3 3. All real numbers except -3, -7/2 Section R5: Rational Expressions

  3. 223 Reference Chapter Simplifying Rational Expressions. Write each numerator and denominator in terms of its factors, then simplify. Example: Write each expression in lowest terms. 1. 2. 3. Section R5: Rational Expressions

  4. 223 Reference Chapter Simplifying Rational Expressions. Write each numerator and denominator in terms of its factors, then simplify. Example: Write each expression in lowest terms. 1. 1/5 2. 1 2m + 6 3. r + 1 r + 3 Section R5: Rational Expressions

  5. 223 Reference Chapter Simplifying Rational Expressions involving Multiplication. Write each numerator and denominator in terms of its factors, cancel out common factors, and simplify. Example: Find each product. 1. 2. 3. Section R5: Rational Expressions

  6. 223 Reference Chapter Simplifying Rational Expressions involving Multiplication. Write each numerator and denominator in terms of its factors, cancel out common factors, and simplify. Example: Find each product. 1. 2a + 8 2. c + 4 c - 4 3. x 4 Section R5: Rational Expressions

  7. 223 Reference Chapter Simplifying Rational Expressions involving Division. First, change division to multiplication by finding the reciprocal of the second rational expression; then, write each numerator and denominator in terms of its factors, cancel out common factors, and simplify. Example: Find each product. 1. 2. 3. Section R5: Rational Expressions

  8. 223 Reference Chapter Simplifying Rational Expressions involving Division. First, change division to multiplication by finding the reciprocal of the second rational expression; then, write each numerator and denominator in terms of its factors, cancel out common factors, and simplify. Example: Find each product. 1. 2b - 6 b + 1 2. 1 3. d^2 + 3d + 9 3 Section R5: Rational Expressions

  9. 223 Reference Chapter Simplifying Rational Expressions involving Addition and/or Subtraction. First, factor all of the numerators and denominators and determine the Least Common Denominator (LCD). Use the LCD to make both fractions have the same denominator, then add and/or subtract the fractions and simplify. Example: Find each sum or difference. 1. 2. Section R5: Rational Expressions

  10. 223 Reference Chapter Simplifying Rational Expressions involving Addition and/or Subtraction. First, factor all of the numerators and denominators and determine the Least Common Denominator (LCD). Use the LCD to make both fractions have the same denominator, then add and/or subtract the fractions and simplify. Example: Find each sum or difference. 1. x^2 – 2x x^2 - 16 2. 3y^2 – 2y - 2 6y^2 Section R5: Rational Expressions

  11. 223 Reference Chapter Simplifying Rational Expressions involving Addition and/or Subtraction. Example: Find each sum or difference. 3. 4. Section R5: Rational Expressions

  12. 223 Reference Chapter Simplifying Rational Expressions involving Addition and/or Subtraction. Example: Find each sum or difference. 3. 7m + 17 m^3 – m^2 – 25 + 1 4. -3a^2 + 3a + 5 a^3 - a Section R5: Rational Expressions

  13. 223 Reference Chapter Simplifying Complex Fractions. The quotient of two rational expressions is referred to as a Complex Fraction. To simplify, multiply both the numerator and denominator by the LCD of all of the fractions. Example: Simplify the expression. Section R5: Rational Expressions

  14. 223 Reference Chapter Simplifying Complex Fractions. The quotient of two rational expressions is referred to as a Complex Fraction. To simplify, multiply both the numerator and denominator by the LCD of all of the fractions. Example: Simplify the expression. 5c + 8 c - 4 Section R5: Rational Expressions

  15. 223 Reference Chapter Simplifying Complex Fractions. Example: Simplify the expression. Section R5: Rational Expressions

  16. 223 Reference Chapter Simplifying Complex Fractions. Example: Simplify the expression. 6k - 5 k + 2 Section R5: Rational Expressions

More Related