Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 7 - Integration Techniques - 7.5 Partial Fractions - 7.5 Exercises: 8

Answer

$$\frac{{10}}{x} + \frac{1}{{x - 1}}$$

Work Step by Step

$$\eqalign{ & \frac{{11x - 10}}{{{x^2} - x}} \cr & {\text{factoring}} \cr & = \frac{{11x - 10}}{{x\left( {x - 1} \right)}} \cr & {\text{partial fraction decomposition}} \cr & \frac{{11x - 10}}{{x\left( {x - 1} \right)}} = \frac{A}{x} + \frac{B}{{x - 1}} \cr & 11x - 10 = A\left( {x - 1} \right) + Bx \cr & {\text{letting }}x = 0 \cr & - 10 = A\left( { - 1} \right) \cr & 10 = A \cr & {\text{letting }}x = 1 \cr & 11 - 10 = A\left( {1 - 1} \right) + B\left( 1 \right) \cr & 1 = B \cr & {\text{substituting the values}} \cr & \frac{A}{x} + \frac{B}{{x - 1}} = \frac{{10}}{x} + \frac{1}{{x - 1}} \cr} $$
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