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130311 7.3 Partial Fractions.notebook
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March 13, 2013
Topic: 7.3: Partial Fractions
Objective and why: "unadd" rational expressions. We need this in calculus to integrate certain functions... I'll show you one at the end of class
Question: What is a partial fraction? What are the four cases of partial fraction decompositions that we covered? DLIQ
Homework: page 745: 18 all, 941 odds(Due Thursday)
Reminders: Due today: 7.2; Missing Work; TEST CORRECTIONS
130311 7.3 Partial Fractions.notebook
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adding rational expressions
finding the partial fraction decomposition, "unadding"
partial fraction
partial fraction
partial fraction
The Idea Behind Partial Fraction Decomposition
130311 7.3 Partial Fractions.notebook
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Each of the two fractions on the right is called a partial fraction. The sum of these fractions is called the partial fraction
decomposition of the rational expression on the lefthand side.
130311 7.3 Partial Fractions.notebook
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The Partial Fraction Decomposition of a
Rational Expression with Distinct Linear Factors in the Denominator
How do I setup a partial fraction decomposition (pfd) for distinct linear denominators?
Each linear factor (in the denominator) produces one partial fraction with a constant as the numerator...
130311 7.3 Partial Fractions.notebook
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Example
130311 7.3 Partial Fractions.notebook
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The Partial Fraction Decomposition of a Rational Expression with Linear Factors in the Denominator, Some of Which are
Repeated
How do I setup PFD for repeated linear factors?
The repeated linear factors produce partial fractions up to the power of the repetition.
What if I have some repeated, some not repeated?
Deal with the nonrepeated as before, and deal with the repeated as we just said...
130311 7.3 Partial Fractions.notebook
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Example
130311 7.3 Partial Fractions.notebook
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The Partial Fraction Decomposition of a Rational Expression with Prime,
Nonrepeated Quadratic Factors in the Denominator
How do I set up my partial fraction if the denominator has a prime quadratic factor?
Please continue you notes on the same paper...
Prime quadratic factors produce partial fractions with linear numerators...
130311 7.3 Partial Fractions.notebook
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Graphing
Example
130311 7.3 Partial Fractions.notebook
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The Partial Fraction Decomposition of a Rational Expression with a Prime, Repeated Quadratic Factor in the
Denominator
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Example
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(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
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