| # | Expression | Partial Fraction Form |
|---|---|---|
| 1. | $\dfrac{px+q}{(x-a)(x-b)},\; a \neq b$ | $\dfrac{A}{x-a}+\dfrac{B}{x-b}$ |
| 2. | $\dfrac{px+q}{(x-a)^2}$ | $\dfrac{A}{x-a}+\dfrac{B}{(x-a)^2}$ |
| 3. | $\dfrac{px+q}{x^2}$ | $\dfrac{A}{x}+\dfrac{B}{x^2}$ |
| 4. | $\dfrac{px^2+qx+r}{(x-a)(x-b)(x-c)}$ | $\dfrac{A}{x-a}+\dfrac{B}{x-b}+\dfrac{C}{x-c}$ |
| 5. | $\dfrac{px^2+qx+r}{(x-a)^2(x-b)}$ | $\dfrac{A}{x-a}+\dfrac{B}{(x-a)^2}+\dfrac{C}{x-b}$ |
| 6. | $\dfrac{px^2+qx+r}{(x-a)(x^2+bx+c)}$ | $\dfrac{A}{x-a}+\dfrac{Bx+C}{x^2+bx+c}$ |
Formulas for the Singapore O-Level Additional Mathematics syllabus