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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
LESSON 5 – SIMPLIFYING RATIONAL VARIABLE EXPRESSIONS

WARM-UP: Factor the following expressions.

a) b)

c) d)

new term
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 
slide3

Investigating RVEs: Workbook (Page 13)

  • Go through the Investigation on Page 13 as a class, using the Nspire Graphing Calculator
slide4

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

slide5

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

rational exponents continued
Rational Exponents (Continued)

EXAMPLE 1: State the restrictions on the variables:

a) b) c)

slide7

Steps for Simplifying RVEs:

  • Factor both the numerator and denominator.
  • Stateall restrictions.
  • Reduce the RVE.
  • NOTE: You must state all restrictions BEFORE you reduce!
rational exponents continued1
Rational Exponents (Continued)

EXAMPLE 2: Simplify and state all restrictions.

a) b)

rational exponents continued2
Rational Exponents (Continued)

(Continued)

EXAMPLE 2: Simplify and state all restrictions.

c) d)

rational exponents continued3
Rational Exponents (Continued)

(Continued)

EXAMPLE 2: Simplify and state all restrictions.

e) f)

rational exponents continued4
Rational Exponents (Continued)

EXAMPLE 3:

  • Use the Nspire to sketch a graph of the function defined by

and

rational exponents continued5
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?
homefun
HomeFUN!!!
  • TEXTBOOK!
    • Pages 40 – 43

# 1 – 6 (alt), 7, 11, 15, 16ac