College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises: 4

Answer

(a) 3 (b) $x(x+1)^2$ (c) $\frac{-2x^{2}+1}{x(x+1)^{2}}$

Work Step by Step

(a) It has three terms, $\displaystyle \frac{1}{x}$, $-\frac{2}{(x+1)}$, and $-\frac{x}{(x+1)^{2}}$. (b) The least common denominator of all the terms is: $x(x+1)^{2}.$ (c) $\displaystyle \frac{1}{x}-\frac{2}{(x+1)}-\frac{x}{(x+1)^{2}}=\frac{(x+1)^{2}}{x(x+1)^{2}}-\frac{2x(x+1)}{(x+1)}-\frac{x(x)}{(x+1)^{2}}=\frac{(x+1)^{2}-2x(x+1)-x^{2}}{x(x+1)^{2}} =\frac{x^{2}+2x+1-2x^{2}-2x-x^{2}}{x(x+1)^{2}}=\frac{-2x^{2}+1}{x(x+1)^{2}}$
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