Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.3 - Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator - Exercise Set: 56

Answer

$\dfrac{12x-6}{x^{2}+3x}\cdot\dfrac{4x^{2}+13x+3}{4x^{2}-1}=\dfrac{6(4x+1)}{x(2x+1)}$

Work Step by Step

$\dfrac{12x-6}{x^{2}+3x}\cdot\dfrac{4x^{2}+13x+3}{4x^{2}-1}$ Factor both rational expressions completely: $\dfrac{12x-6}{x^{2}+3x}\cdot\dfrac{4x^{2}+13x+3}{4x^{2}-1}=\dfrac{6(2x-1)}{x(x+3)}\cdot\dfrac{(x+3)(4x+1)}{(2x-1)(2x+1)}=...$ Evaluate the product and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression: $...=\dfrac{6(2x-1)(x+3)(4x+1)}{x(x+3)(2x-1)(2x+1)}=\dfrac{6(4x+1)}{x(2x+1)}$
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