Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 11 - Rational Expressions and Functions - Common Core Cumulative Standards Review - Selected Response - Page 721: 5

Answer

D.

Work Step by Step

$\frac{x-4}{\frac{x+3}{x-1}}$ In essence, a fraction is a way to write a division. In a fraction, the numerator is the dividend and the denominator is the divisor. Thus, we can rewrite this expression as: $(x-4)\div\frac{x+3}{x-1}$. $(x-4)\div\frac{x+3}{x-1}=(x-4)\times\frac{x-1}{x+3}=\frac{(x-4)(x-1)}{x+3}=\frac{x^2-x-4x+4}{x+3}=\frac{x^2-5x+4}{x+3}$ (choice D).
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