Explanation Given information: The given expression is 10 a 2 − a − 6 + 3 a a 2 + 4 a + 4 . 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 10 a 2 − a − 6 + 3 a a 2 + 4 a + 4 and solve as below: The LCD of the denominators can be found out by factorization of the denominator. Since the factors of a 2 − a − 6 is: a 2 − a − 6 = a 2 − a − 6 = a 2 + 2 a − 3 a − 6 = ( a + 2 ) ( a − 3 ) And the factor of a 2 + 4 a + 4 is: a 2 + 4 a + 4 = a 2 + 4 a + 4 = ( a + 2 ) 2 Therefore, the Least Common Denominator is: LCD = ( a + 2 ) 2 ( a − 3 ) To get the Least Common Denominator in each expression, multiply the each term by a symbol for 1. 10 a 2 − a − 6 + 3 a a 2 + 4 a + 4 = 10 ( a + 2 ) ( a − 3 ) ⋅ ( a + 2 ) ( a + 2 ) + 3 a ( a + 2 ) 2 ⋅ ( a − 3<

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ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 12.4, Problem 60ES

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Chapter 12.4, Problem 59ES

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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 10 a 2 − a − 6 + 3 a a 2 + 4 a + 4 and simplify, if possible.

Solution Summary: The author explains how to calculate the LCD of the denominators by adding and simplifying the expression.

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