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: 29

Answer

$\dfrac{t-4}{t+3}$

Work Step by Step

Adding the numerators and copying the denominator, the given expression, $\dfrac{t^2-5t}{t^2+6t+9}+\dfrac{4t-12}{t^2+6t+9} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{t^2-5t+4t-12}{t^2+6t+9} \\\\= \dfrac{t^2-t-12}{t^2+6t+9} \\\\= \dfrac{(t-4)(t+3)}{(t+3)(t+3)} \\\\= \dfrac{(t-4)(\cancel{t+3})}{(t+3)(\cancel{t+3})} \\\\= \dfrac{t-4}{t+3} .\end{array}

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