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: 12

Answer

$\left\{x|x\gt 1\right\}$

Work Step by Step

The square root is defined only when the radicand (number/expression inside the radical sign) is non-negative. However, since the square root is in the denominator, its value is not allowed to be zero as it will make the whole expression undefined. Thus, to find the values of $x$ for which the given expression is defined, solve the inequality $x-1 \gt 0$ to obtain: $x-1 \gt 0 \\x-1+1 \gt 0+1 \\x \gt 1$ Thus, the domain of the given expression is the set of all real numbers greater than $1$.
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