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: 41



Work Step by Step

$\frac{1}{x+5}+\frac{2}{x-3}$ Find the least common denominator (i.e. $(x+5)(x-3)$) and adjust the fractions: $=\frac{x-3}{(x-3)(x+5)}+\frac{2(x+5)}{(x-3)(x+5)}$ Combine the fractions: $=\frac{x-3+2(x+5)}{(x-3)(x+5)}$ Expand any brackets: $=\frac{x-3+2x+10}{(x-3)(x+5)}$ Collect the like terms: $=\frac{3x+7}{(x-3)(x+5)}$
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