Explanation Given: A complex fraction x − 1 x 2 − 4 1 + 1 x − 2 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: Step 1: Multiply the numerator and the denominator of the complex fraction by the LCD of the fractions in both the numerator and the denominator. Step 2: Simplify Numerator and Denominator separately. Difference of square rule: a 2 − b 2 = ( a + b ) ( a − b ) Calculation: Simplifying a Complex Fraction: Step 1: Find the factors of the Numerator separately by using the difference of square rule. Difference of square rule: a 2 − b 2 = ( a + b ) ( a − b ) Numerator: x − 1 x 2 − 4 = x − 1 ( x + 2 ) ( x − 2 ) Step 2: LCD of Numerator x − 1 x 2 − 4 = x − 1 ( x + 2 ) ( x − 2 ) and Denominator 1 + 1 x − 2 is ( x − 2 ) ( x + 2 ) Multiply the numerator x − 1 x 2 − 4 = x − 1 ( x + 2 ) ( x − 2 ) and the denominator 1 + 1 x − 2 of the complex fraction by the LCD ( x − 2 ) ( x + 2 ) of the fractions in both the numerator and the denominator

15th Edition

ISBN: 9780321978929

Author: Martin-Gay

Publisher: PEARSON

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Chapter 14.7, Problem 31ES

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Simplify the complex fraction x−1x2−4 1+ 1x−2

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Simplify the complex fraction x − 1 x 2 − 4 1 + 1 x − 2

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

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Simplify the complex fraction x−1x2−4 1+ 1x−2

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