Use a system of equations to write the partial fraction decomposition of the rational expression. Solve the system using matrices. 24x2 (x – 1)2(x + 1) A_ x + 1 B + X - 1 (x – 1)2 Step 1

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Use a system of equations to write the partial fraction decomposition of the rational expression. Solve the
system using matrices.
24x2
(x - 1)2(x + 1)
A_
x + 1
B
+
X - 1
(x – 1)2
Step 1
24x2
We are given that the partial fraction decomposition of the rational expression
is
(x - 1)2 (x + 1)
A
B
x + 1
(x – 1)2
X - 1
Multiply each side of the equation by the LCD (x - 1)2 (x + 1) and find the basic equation.
24x2 = A(x – 1)2 + B(x – 1)(x + 1) + C(x + 1)
Expand the basic equation and collect like terms.
24x2 = A(x2 – 2x + 1) + B(x² – 1) + C(x + 1)
24x2
Remember to use capital A and B. x2 + (-2A + C)x +
Remember to use capital A, B and C.
Transcribed Image Text:Use a system of equations to write the partial fraction decomposition of the rational expression. Solve the system using matrices. 24x2 (x - 1)2(x + 1) A_ x + 1 B + X - 1 (x – 1)2 Step 1 24x2 We are given that the partial fraction decomposition of the rational expression is (x - 1)2 (x + 1) A B x + 1 (x – 1)2 X - 1 Multiply each side of the equation by the LCD (x - 1)2 (x + 1) and find the basic equation. 24x2 = A(x – 1)2 + B(x – 1)(x + 1) + C(x + 1) Expand the basic equation and collect like terms. 24x2 = A(x2 – 2x + 1) + B(x² – 1) + C(x + 1) 24x2 Remember to use capital A and B. x2 + (-2A + C)x + Remember to use capital A, B and C.
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