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: 34

Answer

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

Work Step by Step

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