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 - Page 393: 28



Work Step by Step

Subtracting the numerators and copying the denominator, the given expression, $ \dfrac{2a^2+15}{a^2-7a+12}-\dfrac{11a}{a^2-7a+12} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{2a^2+15-11a}{a^2-7a+12} \\\\= \dfrac{2a^2-11a+15}{a^2-7a+12} \\\\= \dfrac{(2a-5)(a-3)}{(a-4)(a-3)} \\\\= \dfrac{(2a-5)(\cancel{a-3})}{(a-4)(\cancel{a-3})} \\\\= \dfrac{2a-5}{a-4} .\end{array}
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