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

Published by Pearson

# Chapter 6 - Rational Expressions and Equations - 6.3 Addition, Subtraction, and Least Common Denominators - 6.3 Exercise Set - Page 393: 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}

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.