Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises - Page 43: 47



Work Step by Step

$u+1+\frac{u}{u+1}$ Convert all elements to a fraction: $=\frac{u}{1}+\frac{1}{1}+\frac{u}{u+1}$ Find the lowest common denominator (i.e. $u+1$) and adjust the fractions accordingly: $=\frac{u\times (u+1)}{1\times (u+1)}+\frac{1\times (u+1)}{1\times (u+1)}+\frac{u}{u+1}$ Expand any brackets: $=\frac{u^{2}+u}{u+1}+\frac{u+1}{u+1}+\frac{u}{u+1}$ Combine fractions: $=\frac{u^{2}+u+u+1+u}{u+1}$ Collect the like terms: $=\frac{u^{2}+3u+1}{u+1}$
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