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: 26

Answer

$\dfrac{1}{x-1}$

Work Step by Step

Adding the numerators and copying the denominator, the given expression, $ \dfrac{x-5}{x^2-4x+3}+\dfrac{2}{x^2-4x+3} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{x-5+2}{x^2-4x+3} \\\\= \dfrac{x-3}{x^2-4x+3} \\\\= \dfrac{x-3}{(x-3)(x-1)} \\\\= \dfrac{\cancel{x-3}}{(\cancel{x-3})(x-1)} \\\\= \dfrac{1}{x-1} .\end{array}
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