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 a b 2 h + c b h 2 − 1 6 b h occurs in strength of materials. Note that, the denominators of the above fractional expression are different. To make the denominators of the fractions equivalent, find the LCD of the denominators. The factors of 6 b h are 2, 3, b and h . Here, the factor b and h appears in all of the denominators and its highest degree is 2 and 2, respectively. Thus, the LCD of the denominators of each fractions is the product of 2, 3, b 2 and h 2 that is 6 b 2 h 2 . To make the resulting denominator in each fraction equal to the LCD, multiply and divide the fraction by the proper quantity. a b 2 h + c b h 2 − 1 6 b h = a b 2 h ⋅ 1 + c b h 2 ⋅ 1 − 1 6 b h ⋅ 1 = a b 2 h ⋅

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 6.6, Problem 66E

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To perform: The indicated operations in the expression ab2h+cbh2−16bh and simplify it.

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Chapter 6.6, Problem 65E

Chapter 6.6, Problem 67E

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For the system consisting of the three planes:plane 1: -4x + 4y - 2z = -8plane 2: 2x + 2y + 4z = 20plane 3: -2x - 3y + z = -1a) Are any of the planes parallel and/or coincident? Justify your answer.b) Determine if the normals are coplanar. What does this tell you about the system?c) Solve the system if possible. Show a complete solution (do not use matrix operations). Classify the system using the terms: consistent, inconsistent, dependent and/or independent.

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Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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 a b 2 h + c b h 2 − 1 6 b h and simplify it.

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To perform: The indicated operations in the expression ab2h+cbh2−16bh and simplify it.

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Chapter 6 Solutions