Explanation Given information: The given expression is 4 − a 25 − a 2 + a + 1 a − 5 . Formula used: The rational numbers can be written in fraction notation as a b where a and b are whole numbers and called as numerator and denominator respectively. To add these rational numbers that don’t shares the same denominator, follow the steps given below: Step 1: Find the least common multiple of the denominators, that number is the least common denominator, LCD. Step 2: Multiply by 1, using the appropriate notation n n for each fraction to express fractions in terms of the LCD. Step 3: Add the numerators and keep the same denominator. Step 4: Simplify, if possible. Calculation: Consider the expression 4 − a 25 − a 2 + a + 1 a − 5 and solve as below: The Least Common Denominator of the denominators can be found out by factorization of the denominator. The factor of 25 − a 2 is: 25 − a 2 = 5 2 − a 2 = ( 5 − a ) ( 5 + a ) It can be noted that ( 5 − a ) is the one factor of ( 25 − a 2 ) . If the denominator of first fraction in the given expression were ( a 2 − 25 ) then ( a − 5 ) could be the factor of both denominators. Therefore, to rewrite the first fraction with denominator a 2 − 25 , just multiply that fraction by − 1 − 1 as below: 4 − a 25 − a 2 + a + 1 a − 5 = 4 − a 25 − a 2 ⋅ − 1 − 1 + a + 1 a − 5 = − ( 4 − a ) a 2 − 25 + a + 1 a − 5 = − 4 + a ( a − 5 ) ( a + 5 ) + a + 1 a − 5 The Least Common Denominator of the expression is ( a − 5 ) ( a + 5 ) . To get the LCD in each expression, multiply the each term by a symbol for 1

16th Edition

ISBN: 9781323235911

Author: BITTINGER

Publisher: Pearson Custom Publishing

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Chapter 12.4, Problem 57ES

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To calculate: The addition of the expression 4−a25−a2+a+1a−5 and simplify, if possible.

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Chapter 12.4, Problem 56ES

Chapter 12.4, Problem 58ES

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Chapter 12 Solutions

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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 the expression 4 − a 25 − a 2 + a + 1 a − 5 and simplify, if possible.

Solution Summary: The author explains how to simplify the expression ab by adding the numerators and keeping the same denominator.

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To calculate: The addition of the expression 4−a25−a2+a+1a−5 and simplify, if possible.

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Chapter 12 Solutions