AHL 1.11—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 $\frac{2x+1}{(x-1)(x+2)}$, we split it into $\frac{1}{x-1}+\frac{1}{x+2}$, which is far easier to integrate or manipulate.