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: 35

Answer

$\frac{2x+7}{3x+4}$

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: $\frac{2x^{2}+17x+35}{3x^{2}+19x+20}$ =$\frac{2x^{2}+7x+10x+35}{3x^{2}+4x+15x+20}$ =$\frac{x(2x+7)+5(2x+7)}{x(3x+4)+5(3x+4)}$ =$\frac{(2x+7)(x+5)}{(3x+4)(x+5)}$ =$\frac{2x+7}{3x+4}$
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