6.2 Multiplying and Dividing Rational Expressions

Multiply rational expressions. Multiplying Rational Expressions The product of the rational expressions and is That is, to multiply rational expressions, multiply the numerators and multiply the denominators. Slide The product of two fractions is found by multiplying the numerators and multiplying the denominators. Rational expressions are multiplied in the same way.

Multiply. Write each answer in lowest terms. Solution: It is also possible to divide out common factors in the numerator and denominator before multiplying the rational expressions. Slide Multiplying Rational Expressions CLASSROOM EXAMPLE 1

Multiply. Write the answer in lowest terms. Solution: Slide Multiplying Rational Expressions CLASSROOM EXAMPLE 2

Multiply. Write the answer in lowest terms. Solution: Slide Multiplying Rational Expressions CLASSROOM EXAMPLE 3

Objective 2 Divide rational expressions. Slide 6.2-8

Divide rational expressions. Dividing Rational Expressions If and are any two rational expressions with then That is, to divide one rational expression by another rational expression, multiply the first rational expression by the reciprocal of the second rational expression. Slide 6.2-9

Solution: Divide. Write each answer in lowest terms. Slide Dividing Rational Expressions CLASSROOM EXAMPLE 4

Divide. Write the answer in lowest terms. Solution: Slide Dividing Rational Expressions CLASSROOM EXAMPLE 5

Divide. Write the answer in lowest terms. Solution: Slide Dividing Rational Expressions CLASSROOM EXAMPLE 6

Divide. Write in the answer in lowest terms. Solution: Remember to write −1 when dividing out factors that are opposite of each other. It may be written in the numerator or denominator, but not both. Slide Dividing Rational Expressions (Factors Are Opposites) CLASSROOM EXAMPLE 7

Multiplying or Dividing Rational Expressions. Multiplying or Dividing Rational Expressions Step 1: Note the operation. If the operation is division, use the definition of division to rewrite it as multiplication. Step 2: Multiply numerators and denominators. Step 3: Factor all numerators and denominators completely. Step 4: Write in lowest terms using the fundamental property. Step 2 and Step 3 may be interchanged based on personal preference. Slide