University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 8 - Section 8.4 - Integration of Rational Functions by Partial Fractions - Exercises - Page 445: 1



Work Step by Step

The form of the partial fraction decomposition is $\frac{5x-13}{(x-3)(x-2)}=\frac{A}{x-3}+\frac{B}{x-2}$ $⇒5x-13= A(x-2)+B(x-3)$ Equating the coefficients of x and the constant term, we get A+B=5 and 2A+3B=13. Solving these equations, we get A=2 and B=3. Thus, $\frac{5x-13}{(x-3)(x-2)}=\frac{2}{x-3}+\frac{3}{x-2}$
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