LESSON 5 – SIMPLIFYING RATIONAL VARIABLE EXPRESSIONS

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# LESSON 5 – SIMPLIFYING RATIONAL VARIABLE EXPRESSIONS - PowerPoint PPT Presentation

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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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
• Examples: ;
• In this lesson, we will see how to SIMPLIFY RVEs 

Investigating RVEs: Workbook (Page 13)

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

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

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)

EXAMPLE 1: State the restrictions on the variables:

a) b) c)

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 (Continued)

EXAMPLE 2: Simplify and state all restrictions.

a) b)

Rational Exponents (Continued)

(Continued)

EXAMPLE 2: Simplify and state all restrictions.

c) d)

Rational Exponents (Continued)

(Continued)

EXAMPLE 2: Simplify and state all restrictions.

e) f)

Rational Exponents (Continued)

EXAMPLE 3:

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

and

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!!!
• TEXTBOOK!
• Pages 40 – 43

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