Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 11 - Rational Expressions and Functions - 11-1 Simplifying Rational Expressions - Lesson Check: 2

Answer

$\frac{-1}{x+3}$ ; x $\neq$ 3, x $\neq$ 5

Work Step by Step

(x-3) (x-5). Begin by factoring the denominator $\frac{x-5}{(x+3)(x-5)}$ plug the factored denominator in. The (x-5) cancels out in numerator and denominator. Equating with zero, we consider the two equations. First, x-5=0, so x=5 Second, x-3=0, so x=3 Hence, $\frac{-1}{x+3}$ ; x $\neq$ 3, x $\neq$ 5 is the final answer.
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