How does the Partial Fraction Decomposition work?

For (ax+b)/((x+p)(x+q)): write as A/(x+p) + B/(x+q) Then: Multiply both sides by denominator Then: Equate coefficients or substitute values Then: Solve for A and B.

Can you give an example of how to use the Partial Fraction Decomposition?

Example: Input (3x+5)/((x+1)(x+2)) gives a result of A/(x+1) + B/(x+2); A=2, B=1.

Is the Partial Fraction Decomposition free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Partial Fraction Decomposition?

Our Partial Fraction Decomposition uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Partial Fraction Decomposition

Partial Fractions Decomposition

(ax + b) / ((x + p)(x + q))

a (numerator coefficient)

b (numerator constant)

p (first root factor)

q (second root factor)

✓Partial Fraction Decomposition

0.3333/(x+1) + 0.6667/(x+-2)

0.3333

0.6667

Partial fraction decomposition breaks a complex rational expression into simpler fractions. It is essential for integration in calculus and for solving differential equations using Laplace transforms.

Symbol	Name	Unit	Description
P(x)	numerator polynomial	—	—
Q(x)	denominator polynomial	—	—
A, B, ...	coefficients of partial fractions	—	—

Denominator Type	Form	Example
Linear factors	A/(x+a)	1/((x+1)(x+2))
Repeated linear	A/(x+a) + B/(x+a)²	1/(x+1)²
Irreducible quadratic	(Ax+B)/(x²+bx+c)	x/(x²+1)

References

›Partial fractions — Khan Academy

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Partial Fraction Decomposition

Partial Fractions Decomposition

✓Partial Fraction Decomposition

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