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: 49



Work Step by Step

$\frac{1}{x^{2}}+\frac{1}{x^{2}+x}$ Factor out the common term from the second fraction: $=\frac{1}{x^{2}}+\frac{1}{x(x+1)}$ Find the least common denominator (i.e. $x^{2}(x+1)$) and adjust the fractions accordingly: $=\frac{1\times (x+1)}{x^{2}(x+1)}+\frac{1\times x}{x^{2}(x+1)}$ Simplify the fractions: $=\frac{x+1}{x^{2}(x+1)}+\frac{x}{x^{2}(x+1)}$ Combine the fractions: $=\frac{x+1+x}{x^{2}(x+1)}$ Collect the like terms: $=\frac{2x+1}{x^{2}(x+1)}$
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