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 - Problem Set 7.1: 39

Answer

$\frac{x+9}{x+3}$

Work Step by Step

Since the numerator and the denominator both consist of a trinomial, we use the rules of factoring trinomials in order to factor them. Then, we cancel out the resultant common factors in the numerator and the denominator: $\frac{7x^{2}+61x-18}{7x^{2}+19x-6}$ =$\frac{7x^{2}-2x+63x-18}{7x^{2}-2x+21x-6}$ =$\frac{x(7x-2)+9(7x-2)}{x(7x-2)+3(7x-2)}$ =$\frac{(7x-2)(x+9)}{(7x-2)(x+3)}$ =$\frac{x+9}{x+3}$
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