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: 46

Answer

$\frac{3x+2}{(x+1)^{2}}$

Work Step by Step

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