What Are Partial Fractions?
Partial Fraction Decomposition
The process of expressing a rational function as a sum of simpler fractions, each with a lower-degree denominator. It is the reverse process of adding fractions over a common denominator.
Partial fractions are a core algebraic technique that appears throughout higher mathematics. In the IB HL course, you will use them primarily to:
- Simplify integration of rational functions (Topic 5)
- Solve certain differential equations
- Investigate series expansions
The key idea: instead of working with a complicated fraction like , we split it into , which is far easier to integrate or manipulate.
Analogy
Think of partial fractions as the reverse of adding fractions. When you add , you combine them into . Partial fractions go the other direction — starting from and splitting it back into . We are "decomposing" rather than "combining".
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