Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Prerequisite Skills Diagnostic Test: 17

Answer

$$\frac{x^2+5x-2}{x(x+1)(x-1)}$$

Work Step by Step

First, factor the denominators of each term $$\frac{x+3}{x^2-1}+\frac{2}{x^2+x}=\frac{x+3}{(x+1)(x-1)}+\frac{2}{x(x+1)}$$ Multiply both the numerator and denominator of the first term by $x$ and the second by $(x-1)$ to obtain a common denominator $$=\frac{x(x+3)}{x(x+1)(x-1)}+\frac{2(x-1)}{x(x+1)(x-1)}$$ Distribute terms in the numerator and add $$=\frac{x^2+3x+2x-2}{x(x+1)(x-1)}=\frac{x^2+5x-2}{x(x+1)(x-1)}$$
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