Explanation Procedure used: Addition or Subtraction of Rational Numbers (Fraction) with unlike denominators: 1. Compute the LCD of the denominators. 2. Write fraction with the LCD as the denominator. 3. Add or subtract the numerators and write the result over the common denominator. 4. Write the result in lowest terms. “ Finding the lowest common denominator ( LCD ) : 1. Find the prime factors of each denominator. 2. For each different prime factor that appears, note the highest power to which it is raised in any one of the denominators. 3. Form the product of all the different prime factors, each raised to the power found in step 2. This product is called the lowest common denominator.” Calculation: The given expression is v + 4 v 2 + 5 v + 4 − v − 2 v 2 − 5 v + 6 . Factor the denominators of the above expression as follows. v + 4 v 2 + 5 v + 4 − v − 2 v 2 − 5 v + 6 = v + 4 v 2 + 4 v + v + 4 − v − 2 v 2 − 3 v − 2 v + 6 = v + 4 ( v 2 + 4 v ) + ( v + 4 ) − v − 2 ( v 2 − 3 v ) − ( 2 v − 6 ) = v + 4 v ( v + 4 ) + ( v + 4 ) − v − 2 v ( v − 3 ) − 2 ( v − 3 ) = v + 4 ( v + 4 ) ( v + 1 ) − v − 2 ( v − 3 ) ( v − 2 ) Cancel like terms. v + 4 v 2 + 5 v + 4 − v − 2 v 2 − 5 v + 6 = ( v + 4 ) ( v + 4 ) ( v + 1 ) − ( v − 2 ) ( v − 3 ) ( v − 2 ) = 1 ( v + 1 ) − 1 ( v − 3 ) Note that, the denominators of the above fractional expression are different

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 6.6, Problem 33E

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To perform: The indicated operations in the expression v+4v2+5v+4−v−2v2−5v+6 and simplify it.

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Chapter 6.6, Problem 32E

Chapter 6.6, Problem 34E

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Basic Technical Mathematics with Calculus (11th Edition)

Ch. 6.1 - Prob. 1PE Ch. 6.1 - Prob. 2PE Ch. 6.1 - Prob. 3PE Ch. 6.1 - Prob. 4PE Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

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To perform: The indicated operations in the expression v + 4 v 2 + 5 v + 4 − v − 2 v 2 − 5 v + 6 and simplify it.

Solution Summary: The author explains how to simplify the expression and calculate the lowest common denominator.

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To perform: The indicated operations in the expression v+4v2+5v+4−v−2v2−5v+6 and simplify it.

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Chapter 6 Solutions