Elementary Algebra

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

Chapter 7 - Algebraic Fractions - 7.3 - Adding and Subtracting Algebraic Fractions - Problem Set 7.3: 80

Answer

$\frac{34}{(3x-4)(2x+3)}$

Work Step by Step

By inspection, we see that the LCM of the denominators is $(2x-1)(3x+1)$. Therefore, we create a common denominator using this LCM and obtain: $\frac{6}{3x-4}-\frac{4}{2x+3}$ =$\frac{6(2x+3)-4(3x-4)}{(3x-4)(2x+3)}$ =$\frac{12x+18-12x+16}{(3x-4)(2x+3)}$ =$\frac{0x+34}{(3x-4)(2x+3)}$ =$\frac{34}{(3x-4)(2x+3)}$
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