College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises: 10

Answer

The domain is $\left\{t| t\ne -2\right\}$.

Work Step by Step

The denominator of an expression is not allowed to be equal to zero. To find the value of $t$ that will make the denominator zero, solve the equation: $3t+6=0 \\3t=-6 \\\frac{3t}{3}=\frac{-6}{3} \\t=-2$ The given expression's denominator will be equal to zero when $t=-2$. Thus, the value of $t$ cannot be $-2$. Therefore, the domain of the given expression is the set of all real numbers except $-2$.
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