Elementary Algebra

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

Chapter 7 - Algebraic Fractions - 7.1 - Simplifying Algebraic Fractions - Concept Quiz 7.1 - Page 280: 7



Work Step by Step

Using the rules of factoring trinomials to factor the quadratic equations in both the numerator and the denominator, we obtain: $\frac{x^{2}+5x-14}{x^{2}-8x+12}$ =$\frac{x^{2}-2x+7x-14}{x^{2}-2x-6x+12}$ =$\frac{x(x-2)+7(x-2)}{x(x-2)-6(x-2)}$ =$\frac{(x-2)(x+7)}{(x-2)(x-6)}$ Now, we cancel out the common factors in the numerator and denominator to simplify: $\frac{(x-2)(x+7)}{(x-2)(x-6)}=\frac{x+7}{x-6}$ Therefore, the statement in the question is true.
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