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: 36

Answer

$-\dfrac{4}{x-1}$

Work Step by Step

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