To determine To calculate: The addition of the rational expression 4 x x − 4 + x + 3 x + 1 . Explanation Given Information: The provided rational expression is 4 x x − 4 + x + 3 x + 1 . Formula used: Follow the steps as mentioned below to add the rational expression with different denominator. Step1: Find out the least common denominator (LCD). Step2: Rewrite the fractions of the rational expression with LCD, by multiplying and dividing the numerator and the denominator with the terms needed to get LCD. Step3: Simplify the numerator by multiplying the terms and leave the denominator in factor form. Step4: Add or subtract the numerators and keep LCD same. Step5: Simplify the expression obtained from step 4 by factoring the numerator, if possible. Calculation: Consider the rational expression, 4 x x − 4 + x + 3 x + 1 The denominators are x − 4 and x + 1 . Take the factors of x − 4 , x − 4 = 1 ⋅ ( x − 4 ) Now take the factors of x + 1 , x + 1 = 1 ⋅ ( x + 1 ) Thus, all the factors from the denominators of the rational expression are 1 , ( x − 4 ) , 1 , ( x + 1 ) To compute the LCD take the product of all the non-repeated factors and take repeated factors one time, as, LCD = ( x − 4 ) ⋅ ( x + 1 ) = ( x − 4 ) ( x + 1 ) To make the fractions of the rational expression with LCD, multiply first term of the expression by x + 1 x + 1 and second term by x − 4 x − 4 . 4 x x − 4 + x + 3 x + 1 = 4 x x − 4 ⋅ x + 1 x + 1 + x + 3 x + 1 ⋅ x − 4 x − 4 Now multiply numerators, 4 x x − 4 ⋅ x + 1 x + 1 + x + 3 x + 1 ⋅ x − 4 x − 4 = 4 x ( x + 1 ) ( x − 4 ) ( x + 1 ) + ( x + 3 ) (

Intermediate Algebra For College Students (9th Edition)

9th Edition

ISBN: 9780321927354

Author: Allen R. Angel, Dennis Runde

Publisher: PEARSON

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Chapter 6.2, Problem 45ES

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To calculate: The addition of the rational expression 4xx−4+x+3x+1.

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Chapter 6.2, Problem 44ES

Chapter 6.2, Problem 46ES

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Chapter 6 Solutions

Intermediate Algebra For College Students (9th Edition)

Ch. 6.1 - Fill in the blanks with the appropriate word,...Ch. 6.1 - Fill in the blanks with the appropriate word,...Ch. 6.1 - Fill in the blanks with the appropriate word,...Ch. 6.1 - Fill in the blanks with the appropriate word,...Ch. 6.1 - Fill in the blanks with the appropriate word,...Ch. 6.1 - Prob. 6ES Ch. 6.1 - Prob. 9ES Ch. 6.1 - Prob. 7ES Ch. 6.1 - Prob. 10ES Ch. 6.1 - Determine the values that are excluded in the...

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