Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - Chapters 1-9 Cumulative Review Problem Set: 14

Answer

$\frac{1}{(x-4)}$

Work Step by Step

We will simplify the expression by first factoring the quadratic equations in both the numerator and the denominators and then cancelling out the resultant common factors: $\frac{x-2}{x^{2}+x-6}\times\frac{x^{2}+6x+9}{x^{2}-x-12}$ =$\frac{x-2}{x^{2}-2x+3x-6}\times\frac{x^{2}+3x+3x+9}{x^{2}+3x-4x-12}$ =$\frac{x-2}{x(x-2)+3(x-2)}\times\frac{x(x+3)+3(x+3)}{x(x+3)-4(x+3)}$ =$\frac{x-2}{(x-2)(x+3)}\times\frac{(x+3)(x+3)}{(x+3)(x-4)}$ =$\frac{x-2}{(x-2)(x+3)}\times\frac{(x+3)}{(x-4)}$ =$\frac{x-2}{(x-2)}\times\frac{1}{(x-4)}$ =$\frac{1}{1}\times\frac{1}{(x-4)}$ =$\frac{1}{(x-4)}$
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