- Home
- NZ Year 10 Maths
- Algebraic Fractions
Partial fraction decomposition
- Intro Lesson9:49
- Lesson: 1a16:29
- Lesson: 1b7:49
- Lesson: 2a14:50
- Lesson: 2b6:36
- Lesson: 38:37
- 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
Do better in math today
20.
Algebraic Fractions
20.1
Simplifying algebraic fractions and restrictions
20.2
Adding and subtracting algebraic fractions
20.3
Multiplying algebraic fractions
20.4
Dividing algebraic fractions
20.5
Solving equations with algebraic fractions
20.6
Applications of equations with algebraic fractions
20.7
Simplifying complex fractions
20.8
Partial fraction decomposition