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LESSON 5 – SIMPLIFYING RATIONAL VARIABLE EXPRESSIONS

LESSON 5 – SIMPLIFYING RATIONAL VARIABLE EXPRESSIONS. WARM-UP : Factor the following expressions. a) b) c) d) . New Term…. RATIONAL VARIABLE EXPRESSIONS. A Rational Variable Expression (RVE) is a quotient where the numerator and denominator are polynomials.

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LESSON 5 – SIMPLIFYING RATIONAL VARIABLE EXPRESSIONS

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  1. LESSON 5 – SIMPLIFYING RATIONAL VARIABLE EXPRESSIONS WARM-UP: Factor the following expressions. a) b) c) d)

  2. New Term… • RATIONAL VARIABLE EXPRESSIONS • A Rational Variable Expression (RVE) is a quotient where the numerator and denominator are polynomials • Examples: ; • In this lesson, we will see how to SIMPLIFY RVEs 

  3. Investigating RVEs: Workbook (Page 13) • Go through the Investigation on Page 13 as a class, using the Nspire Graphing Calculator

  4. Rational Variable Expressions • How can you determine which values of the variable will result in “undefined”? • A value of the variable which makes any factor in the denominator equal to zero gives an “undefined” result. • (This is because dividing by 0 is undefined!) • Example: Undefined for: x = 0 and x = -2

  5. Rational Variable Expressions • NOTE: When we have variables in the denominator of a RVE, there are RESTRICTIONS on those variables!  a RVE is only defined when the denominator  0 (Division by 0 is undefined!!) • RECALL: The zero product property: • If a • b = 0 Then: a = 0 or b = 0 or a = 0 and b = 0

  6. Rational Exponents (Continued) EXAMPLE 1: State the restrictions on the variables: a) b) c)

  7. Steps for Simplifying RVEs: • Factor both the numerator and denominator. • Stateall restrictions. • Reduce the RVE. • NOTE: You must state all restrictions BEFORE you reduce!

  8. Rational Exponents (Continued) EXAMPLE 2: Simplify and state all restrictions. a) b)

  9. Rational Exponents (Continued) (Continued) EXAMPLE 2: Simplify and state all restrictions. c) d)

  10. Rational Exponents (Continued) (Continued) EXAMPLE 2: Simplify and state all restrictions. e) f)

  11. Rational Exponents (Continued) EXAMPLE 3: • Use the Nspire to sketch a graph of the function defined by and

  12. Rational Exponents (Continued) EXAMPLE 3: (Continued) • Describe the similarities and differences of these functions. • What conclusions can you make about the graph of a rational function when the restriction is reduced away?

  13. HomeFUN!!! • TEXTBOOK! • Pages 40 – 43 # 1 – 6 (alt), 7, 11, 15, 16ac

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