Warm- up

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Warm- up

• Factor completely

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Simplify, Multiply and Divide Rational Expressions

• Objectives
• To simplify rational expressions, and
• Simplify complex fractions

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Rational algebraic expressions

• A rational algebraic expression can be expressed
  as the quotient of two polynomials.
• Note The denominator can NEVER be 0.

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Rational Expression

• Property Let a, b, and c be expressions with
  and
• Then the following property applies
•  

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Simplified Form of a Rational Expression

• A rational expression is in SIMPLIFIED FORM if
  its numerator and DENOMINATOR have no common
  factors other than
•  

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procedure

• Factor the numerator and denominator.
• Divide out any factors that are common to both.
• State the excluded values by setting the
  denominator 0 and solving.
• Example

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BIG NO NO

• Factor the numerator and denominator.
• Divide out any factors that are common to both.
• State the excluded values by setting the
  denominator 0 and solving.
• Example

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Simply rational expressions

• Example 1

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Simply rational expressions

• Example 2

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Simplify rational expressions

• Example 3 Simplify

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Simplify rational expressions

• Example 4 Simplify

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Multiply fractions/rational expressions

• Recall to multiply two fractions or rational
  expressions, you first multiply the numerators
  and then multiply the denominators.

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MULTIPLYING PROCEDURE

1. MULTIPLY THE NUMERATORS.
2. MULTIPLY THE DENOMINATORS.
3. WRITE THE NEW FRACTION IN SIMPLIFIED FORM.

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Multiply rational expressions

• Example 5 Multiply
• Recall to multiply two fractions or rational
  expressions, you first multiply the numerators
  and then multiply the denominators.

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Multiply rational expressions

• Example 6 Multiply
• Example 7 Multiply

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Multiply rational expressions

• Example 8 Multiply

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Dividing Procedure

1. Multiply by the reciprocal
2. Simplify.

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Divide rational expressions

• Example 9

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Divide rational expressions

• Example 10 Divide

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Divide rational expressions

• Example 11 Divide

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Divide rational expressions

• Example 12 Divide

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In groups of 4

• Person 1 Write two rational expressions using
  the same variables
• Person 2 Simplify the expression
• Person 3 Multiply the two expressions
• Person 4 Divide the two expressions
• DISCUSS
• ROTATE AND REPREAT

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TOTD

• Explain under what conditions a rational
  polynomial expression is not defined.

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homework

• Kuta worksheet