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Partial fraction decomposition
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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?
- 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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16.
Rational Expressions
16.1
Simplifying rational expressions and restrictions
16.2
Adding and subtracting rational expressions
16.3
Multiplying rational expressions
16.4
Dividing rational expressions
16.5
Solving rational equations
16.6
Applications of rational equations
16.7
Simplifying complex fractions
16.8
Partial fraction decomposition