Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 11 - Rational Expressions and Functions - 11-1 Simplifying Rational Expressions - Practice and Problem-Solving Exercises - Page 667: 30



Work Step by Step

First, find the area of Rectangle A with the Area = Length x Width formula. Then multiply 2x+6 by -3x and distribute: ((2x)(3x) + (6)(3x)) = $6x^{2}$ + 18x. The area of Rectangle A is $6x^{2}$ + 18x. Rectangle B's area is 12 square units greater than Rectangle A, so add 12 to the equation used for the area of Rectangle A. $6x^{2}$ + 18x + 12 To find the width of Rectangle B factor the equation for its area. $6x^{2}$ + 18x + 12 $6(x^{2}$ + 3x + 2) 6(x+2)(x+1) After simplifying, divide the area of Rectangle B by its length x+2. 6(x+2)(x+1) $\div$ (x+2) = 6(x+1) Distribute to get the width of Rectangle B. 6(x+1) = 6x+6
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