Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 5.6, Problem 33WE

To determine

To simplify the given expression.

Expert Solution & Answer

Answer to Problem 33WE

5x(x−3)(x−2)(x+2)

Explanation of Solution

Given:

Expression: 3x2−5x+6+2x2−4

Calculation:

Consider the given expression 3x2−5x+6+2x2−4 ,

Since the denominators of both the fractions are different, find the least common denominator for both the fractions.

Here, least common denominator is (x−3)(x−2)(x+2) , so

3x2−5x+6+2x2−4

=3(x−3)(x−2)+2(x−2)(x+2)

[Factorizing the denominators]

=3⋅(x+2)(x−3)(x−2)⋅(x+2)+2⋅(x−3)(x−2)(x+2)⋅(x−3)

=3(x+2)(x−3)(x−2)(x+2)+2(x−3)(x−3)(x−2)(x+2)

Now, as the denominators of the two fractions are same, simply add the numerators and put the result on the same denominator.

=3(x+2)+2(x−3)(x−3)(x−2)(x+2)

=3x+6+2x−6(x−3)(x−2)(x+2)=3x+6+2x−6(x−3)(x−2)(x+2)=5x(x−3)(x−2)(x+2)

Conclusion:

Therefore, after simplification, the answer is 5x(x−3)(x−2)(x+2) .

Chapter 5.6, Problem 32WE

Chapter 5.6, Problem 34WE

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

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