Differential Equations and Linear Algebra (4th Edition)
4th Edition
ISBN: 9780321964670
Author: Stephen W. Goode, Scott A. Annin
Publisher: PEARSON
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Chapter B, Problem 15P
To determine
The partial fraction decomposition of the given rational function.
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B
B1. If
(x-1) (x+1)² (x-1) ' (x+1) ' (x+1)*
C
using partial fractions, then find the value of 24-2B+2C.
4. Given a rational function: r(x) =
3x2-2x+4
x3-2x–4x+8
Factor the denominator completely. Make sure you justify your answer by showing all the
steps.
a.
Use part (a) to write the form of the partial fraction decomposition for r(x). Make sure you
justify your answer by showing all the steps.
b.
Page 1 of 2
Simplify part (b) to set up a system of linear equations to find the coefficients of the partial
fraction decomposition. Make sure you justify your answer by showing all the steps.
C.
Зx2—2х+5
x3-x2+2x-2
4. Given a rational function: r(x)
Factor the denominator. Make sure you justify your answer by showing all the steps.
а.
b.
Use part (a) to write the form of the partial fraction decomposition for r(x). Make sure you justify
your answer by showing all the steps.
Chapter B Solutions
Differential Equations and Linear Algebra (4th Edition)
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- Expand the following rational function using Partial fractions Step 2 x-1 (Y-1) (x+1) B. 1. (X-1)(x+) X-1 : A(x+1) +B(x-1) (ス-1)(M+) (X-1) (x+1) |- A(x+) + B(x- 1) Please explam 1Hiese Steps in detail ļ 1- x(A+B) + (A-B) Comparing. How do I AtB=0:-0 get to these steps. A -B= 1 0: A+B) A=-B. - B- 13:) ) 13 = - Omay こ (X-1) (x+1) 2(X-1) Ang 고arrow_forward(c) partial fractions of 4x + 2 x³ + 2x² + 2xarrow_forwardThe simplest decomposition of the rational function- 1 into partial (3x=6)(x*-16) fractions is: A B Dx+E + x2+9 A B + (x-3)2 Dx+E + x2+4 x+3 x-3 x+2 x-2 (x-2)2 the above the above A B + (x+2)2 A Dx+E В + x+3 C Dx+E + (x+3)2 x2+9 x² +4 x-3 x-2 x+2 the above the abovearrow_forward
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