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: 33

Answer

$-\dfrac{5}{x-4}$

Work Step by Step

Adding the numerators and copying the denominator, the given expression, $ \dfrac{3-2x}{x^2-6x+8}+\dfrac{7-3x}{x^2-6x+8} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{3-2x+7-3x}{x^2-6x+8} \\\\= \dfrac{10-5x}{x^2-6x+8} \\\\= \dfrac{5(2-x)}{(x-2)(x-4)} \\\\= \dfrac{-5(x-2)}{(x-2)(x-4)} \\\\= \dfrac{-5(\cancel{x-2})}{(\cancel{x-2})(x-4)} \\\\= -\dfrac{5}{x-4} .\end{array}
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