Prealgebra (7th Edition)

Published by Pearson
ISBN 10: 0321955048
ISBN 13: 978-0-32195-504-3

Chapter 4 - Section 4.6 - Complex Fractions and Review of Order of Operations - Exercise Set: 56

Answer

$-\frac{2x}{19}+\frac{8}{19}$

Work Step by Step

$\frac{1-\frac{x}{4}}{2+\frac{3}{8}}$ $=(1-\frac{x}{4})\div(2+\frac{3}{8})$ $=(1-\frac{x}{4})\div(\frac{16}{8}+\frac{3}{8})$ $=(1-\frac{x}{4})\div\frac{19}{8}$ $=(1-\frac{x}{4})\times\frac{8}{19}$ $=\frac{8}{19}(\frac{1}{1}-\frac{x}{4})$ Use the distributive property to distribute $\frac{8}{19}$ to $(\frac{1}{1}-\frac{x}{4})$ $=\frac{8}{19}-\frac{8x}{76}$ $=\frac{8}{19}-\frac{2x}{19}$ $=-\frac{2x}{19}+\frac{8}{19}$ (generally the $x$ term is written before the term with no variable when expressing simplified polynomials)
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