College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.6 - Page 86: 11

Answer

$\frac{y+9}{y-1}$; $y \ne 1, 2$

Work Step by Step

To begin with, we will need to factor the numerator and the denominator: $\frac{(y+9)(y-2)}{(y-1)(y-2)}$ Here, we can see that the $x - 2$ factors cancel out. As a result, we are left with $\frac{y+9}{y-1}$. This still will only hold true as long as we include our domain restrictions from earlier. This means that we must set the original denominator equal to 0: $(y - 1)(y - 2) = 0$ This means, that $y = 1$ and $y = 2$ are both domain restrictions.
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