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Multiplying and Dividing Rational Expressions: A Step-by-Step Guide, Schemes and Mind Maps of Calculus

Columbia Gorge Community College (CGCC)Calculus

A comprehensive guide on how to multiply and divide rational expressions. It includes examples with detailed solutions, following the steps of factoring all numerators and denominators, dividing common factors, and multiplying the remaining factors. The document also covers the concept of reciprocal and its role in dividing rational expressions.

What you will learn

What role does the reciprocal play in dividing rational expressions?
How do you multiply two rational expressions?
What is the process for dividing two rational expressions?

Typology: Schemes and Mind Maps

2021/2022

Uploaded on 09/12/2022

magicphil 🇺🇸

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Section 7.2 Multiplying and Dividing Rational Expressions

Cheon-Sig Lee Page 1

Multiplying Rational Expressions

 The product of two rational expressions is the product of their numerators divided by the

product of their denominators

 If P(x), Q(x), R(x), and S(x) are functions in x, where 𝑄(𝑥)≠0 and 𝑆(𝑥)≠0, then

𝑃(𝑥)

𝑄(𝑥)∙𝑅(𝑥)

𝑆(𝑥)=𝑃(𝑥)∙ 𝑅(𝑥)

𝑄(𝑥)∙ 𝑆(𝑥)

Multiplying Rational Expressions

 Step 1: Factor all numerators and denominators completely

 Step 2: Divide common factor(s)

 Step 3: Multiply the remaining factors.

Dividing Rational Expressions

 Dividing two rational expressions is the product of the first expression and the reciprocal

of the second expression.

 The reciprocal is the multiplicative inverse of the rational expression. The reciprocal is

found by interchanging the numerator and the denominator

 If P(x), Q(x), R(x), and S(x) are functions in x, where 𝑄(𝑥)≠0 and 𝑆(𝑥)≠0, then

𝑃(𝑥)

𝑄(𝑥)∙𝑅(𝑥)

𝑆(𝑥)=𝑃(𝑥)∙ 𝑆(𝑥)

𝑄(𝑥)∙ 𝑅(𝑥)

Excercise

(Solution 1)

𝑥

7∙42

𝑥+ 9 =𝑥

7∙6∙7

𝑥+ 9 =6𝑥

𝑥+ 9

(Solution 2)

Step 1: Factor all numerators and denominators

3𝑥+12 = 3(𝑥+ 4)

8𝑥 − 72 = 8(𝑥 − 9)

Step 2: Dividing Common Factors

𝑥 − 9

𝑥+ 4 ∙3𝑥+12

8𝑥 − 72 =𝑥 − 9

𝑥+ 4 ∙3(𝑥+ 4)

8(𝑥 − 9) =1

1∙3

8

Step 3: Multiply the remain factors

1

1∙3

8=1∙3

1∙8=3

8

Partial preview of the text

Download Multiplying and Dividing Rational Expressions: A Step-by-Step Guide and more Schemes and Mind Maps Calculus in PDF only on Docsity!

Multiplying Rational Expressions

 The product of two rational expressions is the product of their numerators divided by the

product of their denominators

 If P ( x ), Q ( x ), R ( x ), and S ( x ) are functions in x , where 𝑄(𝑥) ≠ 0 and 𝑆(𝑥) ≠ 0 , then

Multiplying Rational Expressions

 Step 1: Factor all numerators and denominators completely

 Step 2: Divide common factor(s)

 Step 3: Multiply the remaining factors.

Dividing Rational Expressions

 Dividing two rational expressions is the product of the first expression and the reciprocal

of the second expression.

 The reciprocal is the multiplicative inverse of the rational expression. The reciprocal is

found by interchanging the numerator and the denominator

 If P ( x ), Q ( x ), R ( x ), and S ( x ) are functions in x , where 𝑄(𝑥) ≠ 0 and 𝑆(𝑥) ≠ 0 , then

Excercise

(Solution 1)

(Solution 2)

Step 1: Factor all numerators and denominators

Step 2: Dividing Common Factors

Step 3: Multiply the remain factors

(Solution 3)

Step 1: Factor all numerators and denominators

By ac -method, we get

2

Step 2: Dividing Common Factors

2

Step 3: Multiply the remain factors

(Solution 4)

Step 1: Factor all numerators and denominators

2

Step 2: Dividing Common Factors

2

Step 3: Multiply the remain factors

(Solution 5)

Step 1: Factor all numerators and denominators

By ac -method, we have

2

Step 2: Dividing Common Factors

2

Step 3: Multiply the remain factors

(Solution 9)

Step 1: Factor all numerators and denominators

No factoring needed

Step 2: Multiply the reciprocal of the second

÷

Step 3: Divide common factor(s)

Step 4: Multiply the remain factors

(Solution 10)

Step 1: Factor all numerators and denominators

Step 2: Multiply the reciprocal of the second

÷

Step 3: Divide common factor(s)

Step 4: Multiply the remain factors

(Solution 11)

Step 1: Factor all numerators and denominators

2

4 is not factorable

Step 2: Multiply the reciprocal of the second

(𝑦 + 4 )(𝑦 − 4 ) ÷

2

Step 3: Divide common factor(s)

2

Step 4: Multiply the remain factors

2

(Solution 12)

Step 1: Factor all numerators and denominators

2

Step 2: Multiply the reciprocal of the second

÷

Step 3: Divide common factor(s)

Step 4: Multiply the remain factors

Multiplying and Dividing Rational Expressions: A Step-by-Step Guide, Schemes and Mind Maps of Calculus

Related documents

Partial preview of the text

Download Multiplying and Dividing Rational Expressions: A Step-by-Step Guide and more Schemes and Mind Maps Calculus in PDF only on Docsity!

Multiplying Rational Expressions

 The product of two rational expressions is the product of their numerators divided by the

product of their denominators

 If P ( x ), Q ( x ), R ( x ), and S ( x ) are functions in x , where 𝑄(𝑥) ≠ 0 and 𝑆(𝑥) ≠ 0 , then

Multiplying Rational Expressions

 Step 1: Factor all numerators and denominators completely

 Step 2: Divide common factor(s)

 Step 3: Multiply the remaining factors.

Dividing Rational Expressions

 Dividing two rational expressions is the product of the first expression and the reciprocal

of the second expression.

 The reciprocal is the multiplicative inverse of the rational expression. The reciprocal is

found by interchanging the numerator and the denominator

 If P ( x ), Q ( x ), R ( x ), and S ( x ) are functions in x , where 𝑄(𝑥) ≠ 0 and 𝑆(𝑥) ≠ 0 , then

Excercise

÷

÷

(𝑦 + 4 )(𝑦 − 4 ) ÷

÷