College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.5 - Rational Expressions - R.5 Exercises - Page 48: 63

Answer

$-\frac{1}{x + 1}$

Work Step by Step

1. Find the LCD of all the fractions: $x + 1$ and $x$ are the denominators, making the LCD $x(x+1)$. 2. Multiply the numerator and denominator by the LCD to clear fractions: $\frac{\frac{1}{x + 1} - \frac{1}{x}}{\frac{1}{x}} = \frac{\left(\frac{1}{x + 1} - \frac{1}{x}\right) \cdot x \cdot (x + 1)}{\frac{1}{x} \cdot x \cdot (x + 1)}$ 3. Distribute: $\frac{\left(\frac{1}{x + 1} - \frac{1}{x}\right) \cdot x \cdot (x + 1)}{\frac{1}{x} \cdot x \cdot (x + 1)}$ = $\frac{\frac{x (x + 1)}{x + 1} - \frac{x (x + 1)}{x}}{\frac{1}{x} x (x + 1)}$ $=\frac{x - (x + 1)}{x + 1}$ $=-\frac{1}{x + 1}$
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