Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Videos

Question

Chapter 5.5, Problem 21WE

To determine

To simplify the given expression.

Expert Solution & Answer

Answer to Problem 21WE

(x+y)(x+3y)

Explanation of Solution

Given:

Expression: 3x2+xy−2y23x2−xy−2y2÷3x2+7xy−6y23x2−2xy−y2÷3x+y3x+2y

Concept used:

To multiply two fractions, simply multiply numerators by each other and denominators by each other and then reduce the fraction if possible.

ab⋅cd→a×cb×d

To divide two fractions, simply flip the second fraction into a reciprocal and change the division sign to a multiplication sign and then multiply the two fractions by multiplying the numerators by each other and denominators by each other. As illustrated below:

ab÷cd→ab×dc→a×db×c

Calculation:

Consider the given expression,

⇒3x2+xy−2y23x2−xy−2y2÷3x2+7xy−6y23x2−2xy−y2÷3x+y3x+2y

⇒3x2+xy−2y23x2−xy−2y2⋅3x2−2xy−y23x2+7xy−6y2⋅3x+2y3x+y [Flipping second and third fractions]

⇒3x2+3xy−2xy−2y23x2−3xy+2xy−2y2×3x2−3xy+xy−y23x2+9xy−2xy−6y2×3x+2y3x+y [Factorizing the fractions]

⇒3x(x+y)−2y(x+y)3x(x−y)+2y(x−y)×3x(x−y)+y(x−y)3x(x+3y)−2y(x+3y)×3x+2y3x+y

⇒(x+y)(3x−2y)(x−y)(3x+2y)×(x−y)(3x+y)(x+3y)(3x−2y)×3x+2y3x+y

⇒(x+y)1×1(x+3y)×11 [Reducing the fractions]

⇒(x+y)×1×11×(x+3y)×1⇒(x+y)(x+3y)

Conclusion:

Therefore, after simplification, the answer is (x+y)(x+3y) .

Chapter 5.5, Problem 20WE

Chapter 5.5, Problem 22WE

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 5.1 - Prob. 1OE Ch. 5.1 - Prob. 2OE Ch. 5.1 - Prob. 3OE Ch. 5.1 - Prob. 4OE Ch. 5.1 - Prob. 5OE Ch. 5.1 - Prob. 6OE Ch. 5.1 - Prob. 7OE Ch. 5.1 - Prob. 8OE Ch. 5.1 - Prob. 9OE Ch. 5.1 - Prob. 10OE

Ch. 5.1 - Prob. 11OE Ch. 5.1 - Prob. 12OE Ch. 5.1 - Prob. 1WE Ch. 5.1 - Prob. 2WE Ch. 5.1 - Prob. 3WE Ch. 5.1 - Prob. 4WE Ch. 5.1 - Prob. 5WE Ch. 5.1 - Prob. 6WE Ch. 5.1 - Prob. 7WE Ch. 5.1 - Prob. 8WE Ch. 5.1 - Prob. 9WE Ch. 5.1 - Prob. 10WE Ch. 5.1 - Prob. 11WE Ch. 5.1 - Prob. 12WE Ch. 5.1 - Prob. 13WE Ch. 5.1 - Prob. 14WE Ch. 5.1 - Prob. 15WE Ch. 5.1 - Prob. 16WE Ch. 5.1 - Prob. 17WE Ch. 5.1 - Prob. 18WE Ch. 5.1 - Prob. 19WE Ch. 5.1 - Prob. 20WE Ch. 5.1 - Prob. 21WE Ch. 5.1 - Prob. 22WE Ch. 5.1 - Prob. 23WE Ch. 5.1 - Prob. 24WE Ch. 5.1 - Prob. 25WE Ch. 5.1 - Prob. 26WE Ch. 5.1 - Prob. 27WE Ch. 5.1 - Prob. 28WE Ch. 5.1 - Prob. 29WE Ch. 5.1 - Prob. 30WE Ch. 5.1 - Prob. 31WE Ch. 5.1 - Prob. 32WE Ch. 5.1 - Prob. 33WE Ch. 5.1 - Prob. 34WE Ch. 5.1 - Prob. 35WE Ch. 5.1 - Prob. 36WE Ch. 5.1 - Prob. 1MRE Ch. 5.1 - Prob. 2MRE Ch. 5.1 - Prob. 3MRE Ch. 5.1 - Prob. 4MRE Ch. 5.1 - Prob. 5MRE Ch. 5.1 - Prob. 6MRE Ch. 5.1 - Prob. 7MRE Ch. 5.1 - Prob. 8MRE Ch. 5.1 - Prob. 9MRE Ch. 5.1 - Prob. 10MRE Ch. 5.1 - 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Prob. 9WE Ch. 5.3 - Prob. 10WE Ch. 5.3 - Prob. 11WE Ch. 5.3 - Prob. 12WE Ch. 5.3 - Prob. 13WE Ch. 5.3 - Prob. 14WE Ch. 5.3 - Prob. 15WE Ch. 5.3 - Prob. 16WE Ch. 5.3 - Prob. 17WE Ch. 5.3 - Prob. 18WE Ch. 5.3 - Prob. 19WE Ch. 5.3 - Prob. 20WE Ch. 5.3 - Prob. 21WE Ch. 5.3 - Prob. 22WE Ch. 5.3 - Prob. 23WE Ch. 5.3 - Prob. 24WE Ch. 5.3 - Prob. 25WE Ch. 5.3 - Prob. 26WE Ch. 5.3 - Prob. 27WE Ch. 5.3 - Prob. 28WE Ch. 5.3 - Prob. 29WE Ch. 5.3 - Prob. 30WE Ch. 5.3 - Prob. 31WE Ch. 5.3 - Prob. 1P Ch. 5.3 - Prob. 2P Ch. 5.3 - Prob. 3P Ch. 5.3 - Prob. 4P Ch. 5.3 - Prob. 5P Ch. 5.3 - Prob. 6P Ch. 5.3 - Prob. 7P Ch. 5.3 - Prob. 8P Ch. 5.3 - Prob. 9P Ch. 5.3 - Prob. 10P Ch. 5.3 - Prob. 11P Ch. 5.3 - Prob. 12P Ch. 5.3 - Prob. 13P Ch. 5.3 - Prob. 14P Ch. 5.3 - Prob. 15P Ch. 5.3 - Prob. 1MRE Ch. 5.3 - Prob. 2MRE Ch. 5.3 - Prob. 3MRE Ch. 5.3 - Prob. 4MRE Ch. 5.3 - Prob. 5MRE Ch. 5.3 - Prob. 6MRE Ch. 5.3 - Prob. 7MRE Ch. 5.3 - Prob. 8MRE Ch. 5.3 - Prob. 9MRE Ch. 5.3 - Prob. 10MRE Ch. 5.3 - Prob. 11MRE Ch. 5.3 - 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