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Partial fraction decomposition
- Intro Lesson9:49
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- Lesson: 1b7:49
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- Lesson: 2b6:36
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- Lesson: 418:13
- Lesson: 5a12:10
- Lesson: 5b11:31
Partial fraction decomposition
Related Concepts: Integration of rational functions by partial fractions
Lessons
∙ Partial fraction decomposition expresses a rational function g(x)f(x), where f(x) and g(x) are polynomials in x, as a sum of simpler fractions.
∙Partial fraction decomposition only applies to proper fractions in which the degree of the numerator is less than that of the denominator.
- IntroductionIntroduction to Partial Fraction Decompositiona)What is partial fraction decomposition?b)When can we perform partial fraction decomposition?
- 1.Case 1: Denominator is a product of linear factors with no repeats
Find the partial fractions of:
a)(x+3)(x−1)x+7b)x2+x4x+3 - 2.Case 2: Denominator is a product of linear factors with repeats
Find the partial fractions of :
a)(x−2)33x2−5b)x2+10x+252x−1 - 3.Case 3: Denominator contains irreducible quadratic factors with no repeats
Find the partial fractions of :
x3−8x2x2+5x+8
- 4.Case 4: Denominator contains irreducible quadratic factors with repeats
Find the partial fractions of:
x(x2+1)23x4+x3+1
- 5.First perform long division, then partial fraction decomposition
Find the partial fractions of:
a)x2−3x2x3−3x2+4xb)x2+6x−162x2+14x+24
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30.
Rational Expressions
30.1
Simplifying rational expressions and restrictions
30.2
Adding and subtracting rational expressions
30.3
Multiplying rational expressions
30.4
Dividing rational expressions
30.5
Solving rational equations
30.6
Applications of rational equations
30.7
Simplifying complex fractions
30.8
Partial fraction decomposition