Explanation Given information: The expression a − 2 3 − a + 4 − a 2 a 2 − 9 . Formula used: To add these arithmetic numbers that don’t shares the same denominator, follow the steps given below: 1. Find the least common multiple of the denominators. That number is the least common denominator, LCD. 2. Multiply by 1, using the appropriate notation n n for each fraction to express fractions in terms of the LCD. 3. Add the numerators and keep the same denominator. 4. Simplify, if possible. Calculation: Consider the expression a − 2 3 − a + 4 − a 2 a 2 − 9 and solve as below: The least common denominator can be found out by factorization of the denominator. The factor of a 2 − 9 is: a 2 − 9 = a 2 − 3 2 = ( a − 3 ) ( a + 3 ) It can be noted that ( a − 3 ) is the one factor of a 2 − 9 . If the denominator of first fraction in the given expression were a − 3 then ( a − 3 ) could be the factor of both denominators. Therefore, to rewrite the second fraction with denominator 3 − a , just multiply that fraction by − 1 − 1 as below: a − 2 3 − a + 4 − a 2 a 2 − 9 = a − 2 3 − a ⋅ − 1 − 1 + 4 − a 2 ( a − 3 ) ( a + 3 ) = − ( a − 2 ) ( a − 3 ) + 4 − a 2 ( a − 3 ) ( a + 3 ) = − a + 2 ( a − 3 ) + 4 − a 2 ( a − 3 ) ( a + 3 ) The least common denominator of the expression is ( a − 3 ) ( a + 3 )

9th Edition

ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 12.4, Problem 56ES

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To calculate: The addition of a−23−a+4−a2a2−9 and simplify, if possible.

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Chapter 12.4, Problem 55ES

Chapter 12.4, Problem 57ES

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Chapter 12 Solutions

Developmental Mathematics (9th Edition)

Ch. 12.1 - Objective 11.3a: Factor trinomials of the type...Ch. 12.1 - Prob. 2SR Ch. 12.1 - Prob. 1DE Ch. 12.1 - Prob. 2DE Ch. 12.1 - Prob. 3DE Ch. 12.1 - Prob. 4DE Ch. 12.1 - Prob. 5DE Ch. 12.1 - Prob. 6DE Ch. 12.1 - Prob. 7DE Ch. 12.1 - Prob. 8DE

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The addition of a − 2 3 − a + 4 − a 2 a 2 − 9 and simplify, if possible.

Solution Summary: The author explains how to add arithmetic numbers that don't share the same denominator.

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To calculate: The addition of a−23−a+4−a2a2−9 and simplify, if possible.

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Chapter 12 Solutions