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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?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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11.
Operations with Algebraic Fractions
11.1
Simplifying algebraic fractions and restrictions
11.2
Adding and subtracting algebraic fractions
11.3
Multiplying algebraic fractions
11.4
Dividing algebraic fractions
11.5
Solving algebraic fraction equations
11.6
Applications of algebraic fraction equations
11.7
Simplifying complex fractions
11.8
Partial fraction decomposition