What this calculator does
Partial fraction decomposition (2 factors) works out splits (ax+b)/((x−p)(x−q)) into simple fractions, including the repeated-root case. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
The inputs explained
| Field | What to enter |
|---|---|
| Numerator: coefficient of x (a) | A number. Starts at 1. |
| Numerator: constant (b) | A number. Starts at 1. |
| Denominator root p (x−p) | A number. Starts at 1. |
| Denominator root q (x−q) | A number. Starts at 2. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with numerator: coefficient of x (a)
Every other input is held at the calculator’s starting values while numerator: coefficient of x (a) varies. Select any row to load that scenario into the calculator.
| Numerator: coefficient of x (a) | Decomposition | A | B |
|---|---|---|---|
| 0.5 | -1.500/(x − 1.00) + 2.000/(x − 2.00) | -1.500 | 2.000 |
| 0.75 | -1.750/(x − 1.00) + 2.500/(x − 2.00) | -1.750 | 2.500 |
| 1 | -2.000/(x − 1.00) + 3.000/(x − 2.00) | -2.000 | 3.000 |
| 1.5 | -2.500/(x − 1.00) + 4.000/(x − 2.00) | -2.500 | 4.000 |
| 2 | -3.000/(x − 1.00) + 5.000/(x − 2.00) | -3.000 | 5.000 |
| 3 | -4.000/(x − 1.00) + 7.000/(x − 2.00) | -4.000 | 7.000 |