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: 10


$\frac{x-4}{3}$, $x\ne4$

Work Step by Step

We must factor the top and bottom separately. First, we factor the top as $(x-4)(x-4)$. Then, we pull out 3 on the bottom, which gives us $3(x-4)$. This gives us the following fraction: $\frac{(x-4)(x-4)}{3(x-4)}$ Then, we are allowed to cancel out the $x - 4$ factors. This leads us to an answer of $\frac{x-4}{3}$. Even though there is no longer an $x - 4$ factor in the denominator, we must still declare that $x\ne 4$ because $x - 4$ was still initially in the bottom of the fraction.
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