Factor completely Warm up Simplify Multiply and Divide

Factor completely: Warm- up

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

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

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

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

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: 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

Example 1 Simply rational expressions

Example #2 Simply rational expressions

Example 3: Simplify: Simplify rational expressions

Example 4: Simplify: Simplify rational expressions

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

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

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: Multiply rational expressions

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

Example 9 Divide rational expressions

Example 10: Divide: Divide rational expressions

Example 11: Divide: Divide rational expressions

Example 12: Divide: Divide rational expressions

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

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

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