Explanation Given: A complex fraction a − 1 + 2 a − 2 2 a − 1 + ( 2 a ) − 1 Concept Used: A rational Expression whose numerator, denominator, or both contains one or more rational expressions is called a complex rational expression or a complex fraction. Simplifying a Complex Fraction: If an expression contains negative exponents, write the expression as an equivalent expression with positive exponents. Step 1: Convert the negative exponents to positive exponent. Step 2: Multiply the numerator and the denominator of the complex fraction by the LCD of the fractions in both the numerator and the denominator. Step 3: Simplify Numerator and Denominator separately. Rule for negative to positive exponent: x − 1 = 1 x ; x − m = 1 x m a ⋅ x − 1 = a x ; a ⋅ x − m = a x m ( a ⋅ x ) − 1 = 1 a ⋅ x ; ( a ⋅ x ) − m = 1 a m ⋅ x m Calculation: Simplifying a Complex Fraction: Step 1: Using the rule: x − 1 = 1 x and a ⋅ x − 1 = a x & ( a ⋅ x ) − 1 = 1 a ⋅ x convert the negative exponents to positive exponent. Rewrite the expression with positive expression: a − 1 + 2 a − 2 2 a − 1 + ( 2 a ) − 1 = 1 a + 2 a 2 2 a + 1 2 a Step 2: LCD of Numerator 1 a + 2 a 2 and Denominator 2 a + 1 2 a is ‘ 2 a 2 ‘ Multiply both the numerator 1 a + 2 a 2 and the denominator 2 a + 1 2 a of the complex fraction by the LCD ‘ 2 a 2 ’ of the fraction

15th Edition

ISBN: 9780321978929

Author: Martin-Gay

Publisher: PEARSON

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Chapter 14.7, Problem 46ES

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Simplify the complex fraction a−1+2a−22a−1+(2a)−1

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Chapter 14.7, Problem 45ES

Chapter 14.7, Problem 47ES

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Simplify the complex fraction a − 1 + 2 a − 2 2 a − 1 + ( 2 a ) − 1

Solution Summary: The author explains how to simplify a complex tion by multiplying the numerator and denominator by the LCD of the tions.

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Simplify the complex fraction a−1+2a−22a−1+(2a)−1

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