Warm- up Factor completely:

Simplify, Multiply and Divide Rational Expressions Objectives: To simplify rational expressions, and Simplify complex fractions

Rational algebraic expressions A rational algebraic expression can be expressed as the quotient of two polynomials. ◦Note: The denominator can NEVER be 0.

Rational Expression Property: Let a, b, and c be expressions with and Then the following property applies:

Simplified Form of a Rational Expression A rational expression is in SIMPLIFIED FORM if its numerator and DENOMINATOR have no common factors other than

procedure 1. Factor the numerator and denominator. 2. Divide out any factors that are common to both. 3. State the excluded values by setting the denominator =0 and solving. Example:

BIG NO NO 1. Factor the numerator and denominator. 2. Divide out any factors that are common to both. 3. State the excluded values by setting the denominator =0 and solving. Example:

Simply rational expressions Example 1

Simply rational expressions Example #2

Simplify rational expressions Example 3: Simplify:

Simplify rational expressions Example 4: Simplify:

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

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

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

Multiply rational expressions Example 6: Multiply: Example 7: Multiply:

Multiply rational expressions Example 8: Multiply:

Dividing Procedure 1. Multiply by the reciprocal 2. Simplify.

Divide rational expressions Example 9

Divide rational expressions Example 10: Divide:

Divide rational expressions Example 11: Divide:

Divide rational expressions Example 12: Divide:

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

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

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