Differential Equations and Linear Algebra (4th Edition)
4th Edition
ISBN: 9780321964670
Author: Stephen W. Goode, Scott A. Annin
Publisher: PEARSON
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Question
Chapter B, Problem 8P
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.
Problem 1.
(A) Let P(x) = 6x3 + 3x2 − x + 3. Use synthetic division to find the value. P(−2)
P(−2) =
(B). Let P(x) = 4x4 − x2 + 4. Use synthetic division to find the value. P (1/3)
P(1/3)
(C) A partial solution set is given for the polynomial equation. Find the complete solution set. (Enter your answers as a comma-separated list.)
x3 + 11x2 + 15x − 27 = 0; {1}
Chapter B Solutions
Differential Equations and Linear Algebra (4th Edition)
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- John found that combining the two rational expressions provided him with the necessary information to draw conclusions on his data. What is the most simplified form of the sum of these expressions? x* +2x-3 *+4x-5 x+4x-5 x-1 x+5 x+4 x-4 x+5 x+4 x+4 x+5 %23 74°F Cloudy o search Del F10 F11 F12 Prt Sc Insert F7 F8 F9 F5 F6 F4 Backspac & O O Oarrow_forwardExpand 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_forwardЗx2—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.arrow_forward
- Express the given rational function in terms of partial fractions. Watch out for any preliminary divisions. 6x + 12 x² X+5x+4 6x + 12 2 X+5x+4 =arrow_forward(c) partial fractions of 4x + 2 x³ + 2x² + 2xarrow_forwardFor questions 9 and 10 we are doing partial fraction decomposition. On the answer key, for #9 we broke up (x^2-4) and (x^2-1) further using the difference of square formula. Why didn't we use this formula in number 10? And instead used Cx+D? How do I know how to differentiate between the methods?arrow_forward
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