Explanation Given: The expression 1 2 x + 1 + 1 4 − 3 4 x 2 − 1 . Formula used: The identity a 2 − b 2 = ( a − b ) ( a + b ) ; Calculation: Consider the expression 1 2 x + 1 + 1 4 − 3 4 x 2 − 1 . Consider the numerator of above expression 1 2 x + 1 + 1 . 1 2 x + 1 + 1 = ( 1 2 x + 1 + 1 ) ⋅ ( 2 x + 1 2 x + 1 ) = ( 1 2 x + 1 ) ⋅ ( 2 x + 1 2 x + 1 ) + 1 ⋅ ( 2 x + 1 2 x + 1 ) = 1 2 x + 1 + 2 x + 1 2 x + 1 Simplified further, 1 2 x + 1 + 1 = 1 + 2 x + 1 2 x + 1 = 2 x + 2 2 x + 1 Now consider the denominator 4 − 3 4 x 2 − 1 . Factorizing 4 x 2 − 1 with the identity a 2 − b 2 = ( a − b ) ( a + b ) ; 4 x 2 − 1 = ( 2 x ) 2 − 1 2 = ( 2 x − 1 ) ( 2 x + 1 ) So, 4 − 3 4 x 2 − 1 = 4 − 3 ( 2 x − 1 ) ( 2 x + 1 ) Multiply the term 4 with the expression ( 2 x − 1 ) ( 2 x + 1 ) ( 2 x − 1 ) ( 2 x + 1 ) , to get; 4 −</

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ISBN: 9780134178967

Author: John Tobey Jr., Jeffrey Slater, Jamie Blair, Jenny Crawford

Publisher: PEARSON

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Chapter 6, Problem 26CT

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To calculate: The simplified form of the expression 12x+1+14−34x2−1.

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Intermediate Algebra (8th Edition)

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The simplified form of the expression 1 2 x + 1 + 1 4 − 3 4 x 2 − 1 .

Solution Summary: The author explains how to calculate the simplified form of the expression 12x++14x2. Then consider the denominator.

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To calculate: The simplified form of the expression 12x+1+14−34x2−1.

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Chapter 6 Solutions