Explanation Given: An expression: 4 − x 4 + 2 x Calculation: In order to rationalize the denominator of an expression, we multiply in the numerator and denominator with such a term/expression such that we don’t have any radicals left in the denominator upon simplifying. 4 − x 4 + 2 x ( Given expression) ⇒ 4 − x 4 + 2 x ⋅ 4 − 2 x 4 − 2 x ( Multiplying by 4 − 2 x in the numerator and denominator ) ⇒ ( 4 − x ) ( 4 − 2 x ) ( 4 + 2 x ) ( 4 − 2 x ) ⇒ 16 − 8 x − 4 x + 2 x ( 4 + 2 x ) ( 4 − 2 x ) ⇒ 16 − 12 x + 2 x ( 4 + 2 x

15th Edition

ISBN: 9780321978929

Author: Martin-Gay

Publisher: PEARSON

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Chapter 17, Problem 12T

To determine

To rationalize:

The denominator of the given expression assuming that all variables represent positive numbers.

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Chapter 17, Problem 11T

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To rationalize: The denominator of the given expression assuming that all variables represent positive numbers.

Solution Summary: The author explains how to rationalize the denominator of an expression assuming that all variables represent positive numbers.