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Pre-Calculus Sec 1.4 Rational Expressions

In this Pre-Calculus section, we explore rational expressions, which are fractional expressions formed from polynomials in the numerator and denominator. We will review how to determine the domain of these expressions and learn techniques to simplify them effectively. Additionally, we cover operations such as multiplication, division, addition, and subtraction of rational expressions, emphasizing the property of fractions needed to combine them correctly. Class activities include working through examples and avoiding common errors, preparing you for advanced algebraic concepts.

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Pre-Calculus Sec 1.4 Rational Expressions

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  1. Pre-CalculusSec 1.4 Rational Expressions Objectives: To review domain To simplify rational expressions

  2. Vocabulary A quotient of two algebraic expressions is a fractional expression. A rational expression is a fractional expression where both the numerator and denominator are polynomials.

  3. Domain The domain of an algebraic expression is the set of real numbers that the variable is permitted to have. Some basic expressions and their domains.

  4. Ex 1. Find the domain of each expression. a) b) c)

  5. Class Work Find the domain of each expression. 1. 2.

  6. Simplifying Rational Expressions Ex 2. Simplify. a) b)

  7. Multiplying Rational Expressions To multiply rational expressions, we use this property of fractions:

  8. Ex 3. Perform the indicated operation and simplfy.

  9. Dividing Rational Expressions To divide rational expressions, we use this property of fractions:

  10. Ex 4. Perform the indicated operation and simplify.

  11. Class Work Multiply or divide and simplify. 3) 4) 5)

  12. Adding & Subtracting Rational Expressions To add or subtract rational expressions, we first find a common denominator and then use this property of fractions:

  13. Ex 4. Perform the indicated operation & simplfy. a) b)

  14. Class Work 6) 7)

  15. Compound Fractions A compound fraction is a fraction in which the numerator, the denominator, or both, are themselves fractional expressions.

  16. Ex 5. Simplify

  17. Common Errors to Avoid

  18. Hw #4 p41 1,4,5,7,10,11,1522,25,27,34,39,42,45,49,51

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