College Algebra (11th Edition)

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

Chapter 5 - Section 5.2 - Matrix Solution of Linear Systems - 5.2 Exercises - Page 500: 48

Answer

$A = 1; B = 4$

Work Step by Step

The given equation is: $$\dfrac{x+4}{x^2} =\dfrac{A}{x}+\dfrac{B}{x^2} ~~~(1)$$ On multiplying equation (1) with $x^2$, we obtain: $$x+4= Ax+B ~~~~(2)$$ Now, we will put $x=0$ in order to eliminate $A$ from equation (2), we obtain: $$B=4$$ Next, we will put $x=1$ in order to eliminate $B$ from equation (2), we obtain: $$1 +4 = A+B \\ 5 =A+4 \\ A=1$$ Our required results are: $$A = 1; B = 4$$
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