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Mastering Multiplying and Dividing Rational Expressions

Learn how to simplify and factor rational expressions, solve complex fractions, and apply ratios to real-life scenarios with examples and explanations. Understand when an expression is undefined and how to handle different types of polynomial expressions effectively.

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Mastering Multiplying and Dividing Rational Expressions

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  1. 8.1 Multiplying and Dividing Rational Expressions

  2. Vocabulary • Rational Expression – a ratio of 2 polynomial expressions. • A rational expression is undefined when the denominator is equal to zero.

  3. Example 1: Simplify • Under what conditions is the expression undefined?

  4. Example 2: Simplify • For what value(s) of p is the expression undefined?

  5. Example 3: Simplify

  6. Example 4: Simplify

  7. With polynomials, factor first! • Example 5: Simplify

  8. Example 6: • Simplify

  9. Example 7: Simplify.

  10. Example 8 • Simplify

  11. Example 9: Simplify.

  12. Example 10: Simplify.

  13. Complex Fractions • Example 11: Simplify

  14. Complex Fractions Example 12: Simplify

  15. Complex Fractions Example 13: Simplify

  16. Example 14 You are considering buying a swimming pool and have narrowed the choices to two—one that is circular and one that is rectangular. The width of the rectangular pool is three times its depth. Its length is 6 feet more than its width. The circular pool has a diameter that is twice the width of the rectangular pool, and it is 2 feet deeper. a. Find the ratio of the volume of the circular pool to the volume of the rectangular pool. b. The volume of the rectangular pool is 2592 cubic feet. How many gallons of water are needed to fill the circular pool if 1 gallon is approximately 0.134 cubic foot?

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