Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. х2 — 3х + 2 4x3 + 7x2 Step 1 The degree of the numerator is less than less than the degree of denominator. 2 - 3x + 2 4x³ + 7x² So, the rational expression is proper proper Step 2 The expression is proper, so factor the denominator. 4x3 + 7x2 = .2 4x + 7 7 Step 3 Since 4x3 + 7x2 = x²(4x + 7), we should include one partial fraction with a constant numerator for each power of x and (4x + 7). So, the partial fraction decomposition must include the sum of three three fractions.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 15T
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Step 4
Therefore, we conclude that the partial fraction decomposition of the given rational expression is as follows.
(Use A, B, and C for your constants.)
Transcribed Image Text:Step 4 Therefore, we conclude that the partial fraction decomposition of the given rational expression is as follows. (Use A, B, and C for your constants.)
Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.
x2 - 3x + 2
4x3 + 7x2
Step 1
The degree of the numerator is less than
less than the degree of denominator.
x2 - 3x + 2
4x3 + 7x2
So, the rational expression
is proper
proper
Step 2
The expression is proper, so factor the denominator.
4x3 + 7x2
2
4x +
7)
Step 3
Since 4x3 + 7x? = x²(4x + 7), we should include one partial fraction with a constant numerator for each
power of x and (4x + 7).
So, the partial fraction decomposition must include the sum of three
three fractions.
Transcribed Image Text:Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. x2 - 3x + 2 4x3 + 7x2 Step 1 The degree of the numerator is less than less than the degree of denominator. x2 - 3x + 2 4x3 + 7x2 So, the rational expression is proper proper Step 2 The expression is proper, so factor the denominator. 4x3 + 7x2 2 4x + 7) Step 3 Since 4x3 + 7x? = x²(4x + 7), we should include one partial fraction with a constant numerator for each power of x and (4x + 7). So, the partial fraction decomposition must include the sum of three three fractions.
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