Partial Fraction Decomposition
Calculate Partial Fraction Decomposition instantly with the exact formula and a worked example.
Partial Fraction Decomposition
A·(x+b)/(x-c)(x-d) — A
b
c
d
Coefficient P of 1/(x − c)
-5
Coefficient Q of 1/(x − d)
10
Decomposition
-5/(x − 1) + 10/(x − 2)
Check: left side at x = max(c, d) + 1
7.5
Check: right side at the same x
7.5
More about: Partial Fraction Decomposition
What it calculates
The “Partial Fraction Decomposition” calculator computes Coefficient P of 1/(x − c) from 4 parameters: a·(x+b)/(x-c)(x-d) — a, b, c, d.
A core calculation for studying, engineering tasks, and checking solutions.
Example calculation
With parameters A·(x+b)/(x-c)(x-d) — A = 5, b = 0, c = 1, d = 2 the result is -5 (Heaviside cover-up method: P = A(c + b)/(c − d), Q = A(d + b)/(d − c); checked by substituting x = max(c, d) + 1).
How to use
- Enter a·(x+b)/(x-c)(x-d) — a, b, c and d — each field above is adjustable with a slider.
- Coefficient P of 1/(x − c) is calculated automatically as you type.
- Check the worked example below to see the formula applied to real numbers.
- Copy the result or bookmark this calculator.
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FAQ
How is Partial Fraction Decomposition calculated?
The Partial Fraction Decomposition calculator computes Coefficient P of 1/(x − c) from a·(x+b)/(x-c)(x-d) — a, b, c, d. Enter your values above and the exact formula is applied instantly; a worked example with real numbers is shown below.
Is the Partial Fraction Decomposition calculator free?
Yes. It is completely free, needs no signup, runs entirely in your browser, and sends no data to any server.
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