PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
Expert Solution & Answer
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Chapter 7.3, Problem 74E
Solution

To calculate : The partial fraction decomposition of 6x23x and support answer graphically.

The partial fraction decomposition of 6x23x is 2x+2x3 .

Given information :

The fraction 6x23x .

Formula used :

For A to be coefficient matrix of a system of n linear equations in n variables given by AX=B . If A1 exists, then system of equations has unique solution X=A1B .

Calculation :

Consider the fraction 6x23x ,

Separate into two fractions with distinct linear denominations.

  6x23x=Ax+Bx3

Multiply both sides with xx3 .

  6=Ax3+Bx

Expand the like terms.

  6=Ax3A+Bx6=A+Bx3A

Using the coefficient and constants, write the system of equations.

  A+B=03A=6

Write the system as matrix equation CX=D where C=1130 , X=AB and D=06 .

Solve for X by multiplying both sides C1 that is X=C1D . Use graphing calculator to find the solution of the system as shown below.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter 7.3, Problem 74E , additional homework tip  1

So, A=2 and B=2 , the partial fraction decomposition is 2x+2x3 .

Graph the functions y1=6x23x and y2=2x+2x3 .

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter 7.3, Problem 74E , additional homework tip  2

Thus, the partial fraction decomposition of 6x23x is 2x+2x3 .

Chapter 7 Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10ECh. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - Prob. 17ECh. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Prob. 43ECh. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - 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