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Grade 12 Math Lab: Analysis & Inference FREE
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Partial Fraction Decomposition
Learning Objectives
- Decompose rational expressions
- Handle repeated and irreducible factors
- Apply to integration
Key Concepts
Partial Fractions
Breaking a fraction into sum of simpler fractions
Cover-Up Method
Quick technique for distinct linear factors
Theory
**For distinct linear factors:**
(px + q)/((x-a)(x-b)) = A/(x-a) + B/(x-b)
**For repeated factors:**
1/(x-a)² = A/(x-a) + B/(x-a)²
**For irreducible quadratic:**
1/((x-a)(x²+bx+c)) = A/(x-a) + (Bx+C)/(x²+bx+c)
**Method:** Multiply both sides by denominator, then solve for constants.
Examples
Decompose (3x+5)/((x+1)(x+2))
Solution: A/(x+1) + B/(x+2). A=2, B=1. Answer: 2/(x+1) + 1/(x+2)