Partial Fraction Decomposition Calculator
Split a fraction over (x-p)(x-q) into two simple fractions.
Enter your values
Enter the numerator slope (0 if constant) you are working with.
Enter the numerator constant you are working with.
Enter the root p you are working with.
Enter the root q you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- A
- 1.6667
- B
- -1.6667
- Decomposition
- 1.6667/(x-1) + -1.6667/(x--2)
Quick answer
A = N(p)/(p-q) and B = N(q)/(q-p) for a linear numerator N(x), using the cover-up method.
A/(x-p) + B/(x-q)
At a glance
| What it does | Split a fraction over (x-p)(x-q) into two simple fractions. |
|---|---|
| Category | Math |
| Inputs needed | Numerator slope (0 if constant), Numerator constant, Root p, Root q |
| Main output | A |
| Formula | A/(x-p) + B/(x-q) |
| Cost | Free — no sign-up, no download |
How to use the Partial Fraction Decomposition Calculator
- 1Enter the numerator as a linear expression (or a constant if the slope is 0).
- 2Enter the two distinct roots p and q of the denominator.
- 3The cover-up method gives A and B directly.
Inputs explained
- Numerator slope (0 if constant)
- Enter the numerator slope (0 if constant) you are working with.
- Numerator constant
- Enter the numerator constant you are working with.
- Root p
- Enter the root p you are working with.
- Root q
- Enter the root q you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Numerator slope (0 if constant)0
- Numerator constant5
- Root p1
- Root q-2
Results
- A1.6667
- B-1.6667
- Decomposition1.6667/(x-1) + -1.6667/(x--2)
Frequently asked questions
What if p equals q?
The denominator has a repeated root, which needs a different decomposition form (A/(x-p) + B/(x-p)^2).
Can the numerator be quadratic?
This tool handles a linear numerator; quadratic numerators need an extra term.
What do I need to enter into the Partial Fraction Decomposition Calculator?
Just 4 values: numerator slope (0 if constant), numerator constant, root p, root q. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Partial Fraction Decomposition Calculator work out the answer?
A = N(p)/(p-q) and B = N(q)/(q-p) for a linear numerator N(x), using the cover-up method. It applies the formula A/(x-p) + B/(x-q) and shows the working so you can check each step by hand.
Is the Partial Fraction Decomposition Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.