Explanation Given: The expression 3 k 2 k 2 + 3 k − 2 − 2 k 2 k 2 − 7 k + 3 . Explanation: Consider the following expression: 3 k 2 k 2 + 3 k − 2 − 2 k 2 k 2 − 7 k + 3 Factorize the denominators as follows: The factorization of equation 2 k 2 + 3 k − 2 will be as follows: The factors of 2 k 2 are k and 2 k and the factors of − 2 are –2 and 1, –1 and 2. Use first set of factors for both the terms and check whether the multiplication holds. ( 2 k − 1 ) ( k + 2 ) = 2 k ⋅ k + 2 k ⋅ 2 − 1 ⋅ k − 1 ⋅ 2 = 2 k 2 + 4 k − k − 2 = 2 k 2 + 3 k − 2 So, this factorization holds. Similarly, for equation 2 k 2 − 7 k + 3 , factorization will be as follows: The factors of 2 k 2 are k and 2 k and the factors of 3 are 3 and 1. Use first set of factors for both the terms and check whether the multiplication holds. ( 2 k − 1 ) ( k − 3 ) = 2 k ⋅ k − 2 k ⋅ 3 − 1 ⋅ k + 1 ⋅ 3 = 2 k 2 − 6 k − k + 3 = 2 k 2 − 7 k + 3 So, this factorization holds. 3 k 2 k 2 + 3 k − 2 − 2 k 2 k 2 − 7 k + 3 = 3 k ( 2 k − 1 ) ( k + 2 ) − 2 k ( 2 k − 1 ) ( k − 3 ) Convert both the fractions to like fractions with the denominator (2 k – 1)( k + 1)( k – 3)as follows: 3 k ( 2 k − 1 ) ( k + 2 ) − 2 k

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter R.3, Problem 35E

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The simplified form of the expression 3k2k2+3k−2−2k2k2−7k+3.

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Chapter R.3, Problem 34E

Chapter R.3, Problem 36E

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The simplified form of the expression 3 k 2 k 2 + 3 k − 2 − 2 k 2 k 2 − 7 k + 3 .

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The simplified form of the expression 3k2k2+3k−2−2k2k2−7k+3.

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