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 13P
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.
x* + 9x2 + x + 2
is
The rational function
improper
and the partial fraction can be written as:
x2 + 9
Ax + B
where A=
[ Select ]
and B =
[ Select ]
x2 + 9
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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- 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}arrow_forwardJohn 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_forward(c) partial fractions of 4x + 2 x³ + 2x² + 2xarrow_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_forward4. 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.arrow_forwardWrite the partial fraction decomposition of the following rational expression. 4x2 + 15x + 42 x(x - 7)(x- 6) 4x2 + 15x + 42 %D X(x - 7)(x - 6)arrow_forward
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