Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 6 - Rational Expressions and Equations - 6.3 Addition, Subtraction, and Least Common Denominators - 6.3 Exercise Set: 27

Answer

$\dfrac{(3a-7)(a-2)}{(a+6)(a-1)}$

Work Step by Step

Subtracting the numerators and copying the denominator, the given expression, $ \dfrac{3a^2+14}{a^2+5a-6}-\dfrac{13a}{a^2+5a-6} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{3a^2+14-13a}{a^2+5a-6} \\\\= \dfrac{3a^2-13a+14}{a^2+5a-6} \\\\= \dfrac{(3a-7)(a-2)}{(a+6)(a-1)} .\end{array}
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