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Mastering Rational Expressions and Complex Fractions in Algebra 2B

Learn how to simplify rational expressions, complex fractions, and master factoring techniques in algebra. Practice multiplying, dividing polynomials, and solving rational equations effectively.

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Mastering Rational Expressions and Complex Fractions in Algebra 2B

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  1. Algebra 2B Chapter 9

  2. Lesson 9.1 Learning Targets: • I can simplify Rational Expressions • I can simplify complex fractions

  3. Vocabulary Rational Expression: It’s the ratio of two polynomial expressions • Examples: • Complex Fraction: It’s a rational expression whose • numerator and/or denominator • contains a rational expression. • Examples:

  4. Multiplying Rational Expressions: Dividing Rational Expressions: Review: How to multiply and divide monomials: How to multiply, divide and find the power of a power: How to factor polynomials:

  5. Summary of Factoring Techniques • For all polynomials, first factor out the greatest common factor (GCF). • For a binomial, check to see if it is any of the following: • difference of squares: x2 − y2 = ( x + y) ( x − y) • difference of cubes: x3 − y3 = ( x − y) ( x2 + xy + y2) • sum of cubes: x3 + y3 = ( x + y) ( x2 − xy + y2) • For a trinomial, use the T • ax2 + bx + c:

  6. Step1: Factor the numerator and denominator completely Step 2: Reduce any common factors Step 3: Simplify 2

  7. Step1: Factor the numerator and denominator completely Step 2: Reduce any common factors Step 3: Simplify 2

  8. Step1: Make into a multiplication problem Step2: Factor the numerator and denominator completely Step 3: Reduce any common factors Step 4: Simplify

  9. Step1: Make into a multiplication problem 3 Step2: Factor the numerator and denominator completely Step 3: Reduce any common factors Step 4: Simplify

  10. 2 2 Continue factoring!!!

  11. Closure 9.1(in class):

  12. Transparency 2 Click the mouse button or press the Space Bar to display the answers.

  13. Transparency 2a

  14. Lesson 9.2 Learning Targets : • I can determine the LCM of polynomials • I can add and subtract rational expressions

  15. Vocabulary To add and subtract Rational Expressions: To find equivalent fractions with the same denominator, we need the LCM.

  16. Your Turn:

  17. Your Turn:

  18. Your Turn:

  19. Your Turn:

  20. Closure Lesson 9.2 (in class):

  21. Transparency 3 Click the mouse button or press the Space Bar to display the answers.

  22. Transparency 3a

  23. Lesson 9.6 Learning Targets : • I can solve Rational Equations

  24. Vocabulary A rational equationis ____________________________________________ ____________________________________________________________ Hint: When solving a rational equation, eliminate the fractions first! Check the solutions in the original equation

  25. Warm-up 9.3 4. 5.

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