PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Question
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Chapter 7.3, Problem 58E
To determine

To write the Partial fraction decomposition of the rational expression 14x2−9 .

Expert Solution & Answer
Check Mark

Answer to Problem 58E

The partial fraction of expansion is −16(2x+3)+16(2x−3)

Explanation of Solution

Given information:

The rational expression is 14x2−9

The rational expression is 14x2−9 .

Here the denominator can be expressed in terms of product of linear factors and the given rational expression can be expressed as sum of partial fraction.

  14x2−9=1(2x)2−(3)2=1(2x+3)(2x−3)=A(2x+3)+B(2x−3)

where A and B are the coefficients.

Now, for finding the value of coefficients A and B

  14x2−9=1(2x)2−(3)2=1(2x+3)(2x−3)1(2x+3)(2x−3)=A(2x+3)+B(2x−3)=A(2x−3)+B(2x+3)(2x+3)(2x−3)1=A(2x−3)+B(2x+3)1=x(2A+2B)+(−3A+3B)

Comparing coefficients of x

  2A+2B=0A=−B

Comparing constant terms in the equation

  −3A+3B=1−3(−B)+3B=16B=1B=16A=−16

therefore, 14x2−9=−1/6(2x+3)+1/6(2x−3)=−16(2x+3)+16(2x−3)

Checking algebraically,

  14x2−9=−16(2x+3)+16(2x−3)=−(2x−3)+(2x+3)6(2x+3)(2x−3)=−(2x−3)+(2x+3)6(2x+3)(2x−3)=−2x+3+2x+36(2x+3)(2x−3)=1(2x+3)(2x−3)=14x2−9

Checking Graphically,

  14x2−9

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 7.3, Problem 58E , additional homework tip 1

  −16(2x+3)+16(2x−3)

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 7.3, Problem 58E , additional homework tip 2

Interpretation:

The graph of rational expression and partial fraction is same hence graphically it is proved that 14x2−9=−16(2x+3)+16(2x−3)

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Chapter 7.3, Problem 59E

Chapter 7 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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. 10E
Ch. 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 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.1 - Prob. 63ECh. 7.1 - 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Prob. 38ECh. 7.6 - Prob. 39ECh. 7.6 - Prob. 40ECh. 7.6 - Prob. 41ECh. 7.6 - Prob. 42ECh. 7.6 - Prob. 43ECh. 7.6 - Prob. 44ECh. 7.6 - Prob. 45ECh. 7.6 - Prob. 46ECh. 7.6 - Prob. 47ECh. 7.6 - Prob. 48ECh. 7.6 - Prob. 49ECh. 7.6 - Prob. 50ECh. 7.6 - Prob. 51ECh. 7.6 - Prob. 52ECh. 7.6 - Prob. 53ECh. 7.6 - Prob. 54ECh. 7.6 - Prob. 55ECh. 7.6 - Prob. 56ECh. 7.6 - Prob. 57ECh. 7.6 - Prob. 58ECh. 7.6 - Prob. 59ECh. 7.6 - Prob. 60ECh. 7.6 - Prob. 61ECh. 7.6 - Prob. 62ECh. 7.6 - Prob. 64ECh. 7.6 - Prob. 65ECh. 7.6 - Prob. 66ECh. 7.6 - Prob. 67ECh. 7.6 - Prob. 68ECh. 7.6 - Prob. 69ECh. 7.6 - Prob. 70ECh. 7.6 - Prob. 71ECh. 7.6 - Prob. 72ECh. 7.6 - Prob. 73ECh. 7.6 - Prob. 74ECh. 7.6 - Prob. 75ECh. 7.6 - Prob. 76ECh. 7.7 - Prob. 1ECh. 7.7 - Prob. 2ECh. 7.7 - Prob. 3ECh. 7.7 - Prob. 4ECh. 7.7 - Prob. 5ECh. 7.7 - Prob. 6ECh. 7.7 - Prob. 7ECh. 7.7 - Prob. 8ECh. 7.7 - Prob. 9ECh. 7.7 - Prob. 10ECh. 7.7 - Prob. 11ECh. 7.7 - Prob. 12ECh. 7.7 - Prob. 13ECh. 7.7 - Prob. 14ECh. 7.7 - Prob. 15ECh. 7.7 - Prob. 16ECh. 7.7 - Prob. 17ECh. 7.7 - Prob. 18ECh. 7.7 - Prob. 19ECh. 7.7 - Prob. 20ECh. 7.7 - Prob. 21ECh. 7.7 - Prob. 22ECh. 7.7 - Prob. 23ECh. 7.7 - Prob. 24ECh. 7.7 - Prob. 25ECh. 7.7 - Prob. 26ECh. 7.7 - Prob. 27ECh. 7.7 - Prob. 28ECh. 7.7 - Prob. 29ECh. 7.7 - Prob. 30ECh. 7.7 - Prob. 31ECh. 7.7 - Prob. 32ECh. 7.7 - Prob. 33ECh. 7.7 - Prob. 34ECh. 7.7 - Prob. 35ECh. 7.7 - Prob. 36ECh. 7.7 - Prob. 37ECh. 7.7 - Prob. 38ECh. 7.7 - Prob. 39ECh. 7.7 - Prob. 40ECh. 7.7 - Prob. 41ECh. 7.7 - Prob. 42ECh. 7.7 - Prob. 43ECh. 7.7 - Prob. 44ECh. 7.7 - Prob. 45ECh. 7.7 - Prob. 46ECh. 7.7 - Prob. 47ECh. 7.7 - Prob. 48ECh. 7.7 - Prob. 49ECh. 7.7 - Prob. 50ECh. 7.7 - Prob. 51ECh. 7.7 - Prob. 52ECh. 7.7 - Prob. 53ECh. 7.7 - Prob. 54ECh. 7.7 - Prob. 55ECh. 7.7 - Prob. 56ECh. 7.7 - Prob. 57ECh. 7.7 - Prob. 58ECh. 7.7 - Prob. 59ECh. 7.7 - Prob. 60ECh. 7.7 - Prob. 61ECh. 7.7 - Prob. 62ECh. 7.7 - Prob. 63ECh. 7.7 - Prob. 64ECh. 7.7 - Prob. 65ECh. 7.7 - Prob. 66ECh. 7.7 - Prob. 67ECh. 7.7 - Prob. 68ECh. 7.7 - Prob. 69ECh. 7.7 - Prob. 70ECh. 7.7 - Prob. 71ECh. 7.7 - Prob. 72ECh. 7.7 - Prob. 73ECh. 7.7 - Prob. 74ECh. 7.7 - Prob. 75ECh. 7.7 - Prob. 76ECh. 7.7 - Prob. 77ECh. 7.7 - Prob. 78ECh. 7.7 - Prob. 79ECh. 7.7 - Prob. 80ECh. 7.7 - Prob. 81ECh. 7.7 - Prob. 82ECh. 7.7 - Prob. 83ECh. 7.7 - Prob. 84ECh. 7.7 - Prob. 85ECh. 7.7 - Prob. 86ECh. 7.7 - Prob. 87ECh. 7.7 - Prob. 88ECh. 7.8 - Prob. 1ECh. 7.8 - Prob. 2ECh. 7.8 - Prob. 3ECh. 7.8 - Prob. 4ECh. 7.8 - Prob. 5ECh. 7.8 - Prob. 6ECh. 7.8 - Prob. 7ECh. 7.8 - Prob. 8ECh. 7.8 - Prob. 9ECh. 7.8 - Prob. 10ECh. 7.8 - Prob. 11ECh. 7.8 - Prob. 12ECh. 7.8 - Prob. 13ECh. 7.8 - Prob. 14ECh. 7.8 - Prob. 15ECh. 7.8 - Prob. 16ECh. 7.8 - Prob. 17ECh. 7.8 - Prob. 18ECh. 7.8 - Prob. 19ECh. 7.8 - Prob. 20ECh. 7.8 - Prob. 21ECh. 7.8 - Prob. 22ECh. 7.8 - Prob. 23ECh. 7.8 - Prob. 24ECh. 7.8 - Prob. 25ECh. 7.8 - Prob. 26ECh. 7.8 - Prob. 27ECh. 7.8 - Prob. 28ECh. 7.8 - Prob. 29ECh. 7.8 - Prob. 30ECh. 7.8 - Prob. 31ECh. 7.8 - Prob. 32ECh. 7.8 - Prob. 33ECh. 7.8 - Prob. 34ECh. 7.8 - Prob. 35ECh. 7.8 - Prob. 36ECh. 7.8 - Prob. 41ECh. 7.8 - Prob. 42ECh. 7.8 - Prob. 43ECh. 7.8 - Prob. 44ECh. 7.8 - Prob. 45ECh. 7.8 - Prob. 46ECh. 7.8 - Prob. 47ECh. 7.8 - Prob. 48ECh. 7 - Prob. 1CRCh. 7 - Prob. 2CRCh. 7 - Prob. 3CRCh. 7 - Prob. 4CRCh. 7 - Prob. 5CRCh. 7 - Prob. 6CRCh. 7 - Prob. 7CRCh. 7 - Prob. 8CRCh. 7 - Prob. 9CRCh. 7 - Prob. 10CRCh. 7 - Prob. 11CRCh. 7 - Prob. 12CRCh. 7 - Prob. 13CRCh. 7 - Prob. 14CRCh. 7 - Prob. 15CRCh. 7 - Prob. 16CRCh. 7 - Prob. 17CRCh. 7 - Prob. 18CRCh. 7 - Prob. 19CRCh. 7 - Prob. 20CRCh. 7 - Prob. 21CRCh. 7 - Prob. 22CRCh. 7 - Prob. 23CRCh. 7 - Prob. 24CRCh. 7 - Prob. 25CRCh. 7 - Prob. 26CRCh. 7 - Prob. 27CRCh. 7 - Prob. 28CRCh. 7 - Prob. 29CRCh. 7 - Prob. 30CRCh. 7 - Prob. 31CRCh. 7 - Prob. 32CRCh. 7 - Prob. 33CRCh. 7 - Prob. 34CRCh. 7 - Prob. 35CRCh. 7 - Prob. 36CRCh. 7 - Prob. 37CRCh. 7 - Prob. 38CRCh. 7 - Prob. 39CRCh. 7 - Prob. 40CRCh. 7 - Prob. 41CRCh. 7 - Prob. 42CRCh. 7 - Prob. 43CRCh. 7 - Prob. 44CRCh. 7 - Prob. 45CRCh. 7 - Prob. 46CRCh. 7 - Prob. 47CRCh. 7 - Prob. 48CRCh. 7 - Prob. 49CRCh. 7 - Prob. 50CRCh. 7 - Prob. 51CRCh. 7 - Prob. 52CRCh. 7 - Prob. 53CRCh. 7 - Prob. 54CRCh. 7 - Prob. 55CRCh. 7 - Prob. 56CRCh. 7 - Prob. 57CRCh. 7 - Prob. 58CRCh. 7 - Prob. 59CRCh. 7 - Prob. 60CRCh. 7 - Prob. 61CRCh. 7 - Prob. 62CRCh. 7 - Prob. 63CRCh. 7 - Prob. 64CRCh. 7 - Prob. 65CRCh. 7 - Prob. 66CRCh. 7 - Prob. 67CRCh. 7 - Prob. 68CRCh. 7 - Prob. 69CRCh. 7 - Prob. 70CRCh. 7 - Prob. 71CRCh. 7 - Prob. 72CRCh. 7 - Prob. 73CRCh. 7 - Prob. 74CRCh. 7 - Prob. 75CRCh. 7 - Prob. 76CRCh. 7 - Prob. 77CRCh. 7 - Prob. 78CRCh. 7 - Prob. 79CRCh. 7 - Prob. 80CRCh. 7 - Prob. 81CRCh. 7 - Prob. 82CRCh. 7 - Prob. 83CRCh. 7 - Prob. 84CRCh. 7 - Prob. 85CRCh. 7 - Prob. 86CRCh. 7 - Prob. 87CRCh. 7 - Prob. 88CRCh. 7 - Prob. 89CRCh. 7 - Prob. 90CRCh. 7 - Prob. 91CRCh. 7 - Prob. 92CRCh. 7 - Prob. 93CRCh. 7 - Prob. 94CRCh. 7 - Prob. 95CRCh. 7 - Prob. 96CRCh. 7 - Prob. 97CRCh. 7 - Prob. 98CRCh. 7 - Prob. 99CRCh. 7 - Prob. 100CRCh. 7 - Prob. 101CRCh. 7 - Prob. 102CRCh. 7 - Prob. 103CRCh. 7 - Prob. 104CRCh. 7 - Prob. 105CRCh. 7 - Prob. 106CRCh. 7 - Prob. 107CRCh. 7 - Prob. 108CRCh. 7 - Prob. 109CRCh. 7 - Prob. 110CRCh. 7 - Prob. 111CRCh. 7 - Prob. 112CRCh. 7 - Prob. 113CRCh. 7 - Prob. 114CRCh. 7 - Prob. 115CRCh. 7 - Prob. 116CRCh. 7 - Prob. 117CRCh. 7 - Prob. 118CRCh. 7 - Prob. 119CRCh. 7 - Prob. 120CRCh. 7 - Prob. 121CRCh. 7 - Prob. 122CRCh. 7 - Prob. 123CRCh. 7 - Prob. 124CRCh. 7 - Prob. 125CRCh. 7 - Prob. 126CRCh. 7 - Prob. 127CRCh. 7 - Prob. 128CRCh. 7 - Prob. 129CRCh. 7 - Prob. 130CRCh. 7 - Prob. 131CRCh. 7 - Prob. 132CRCh. 7 - Prob. 133CRCh. 7 - Prob. 134CRCh. 7 - Prob. 135CRCh. 7 - Prob. 136CRCh. 7 - Prob. 137CRCh. 7 - Prob. 138CRCh. 7 - Prob. 139CRCh. 7 - Prob. 140CRCh. 7 - Prob. 141CRCh. 7 - Prob. 1CTCh. 7 - Prob. 2CTCh. 7 - Prob. 3CTCh. 7 - Prob. 4CTCh. 7 - Prob. 5CTCh. 7 - Prob. 6CTCh. 7 - Prob. 7CTCh. 7 - Prob. 8CTCh. 7 - Prob. 9CTCh. 7 - Prob. 10CTCh. 7 - Prob. 11CTCh. 7 - Prob. 12CTCh. 7 - Prob. 13CTCh. 7 - Prob. 14CTCh. 7 - Prob. 15CTCh. 7 - Prob. 16CTCh. 7 - Prob. 17CT
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