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Partial Fraction Decomposition Calculator

Breaks a rational function into simple fractions, covering distinct linear factors, repeated factors and irreducible quadratics. The setup and the linear system solved for the coefficients are both shown, since that is the part being learned.

Related tools

All Calculus tools →
Partial Derivative CalculatorCompute partial and mixed derivatives of a multivariable function symbolically.LU Decomposition CalculatorFactor a square matrix into a lower L and upper U triangular matrix (Doolittle method).Fraction CalculatorAdd, subtract, multiply or divide two fractions and get the reduced result plus its decimal value.Continued fraction calculatorExpand a number into its continued fraction [a₀; a₁, a₂, …] and list the convergents — the best rational approximations at each step. Feed it a decimal, an exact fraction a/b, or a square root √k: rationals terminate, √k is periodic, and irrationals stream on to the term cap. Continued fractions give the closest fractions for a given size of denominator and reveal the hidden structure of numbers like the golden ratio and π.Fraction simplifierReduce a fraction to its simplest form and see its decimal value.Percent to Fraction CalculatorConvert a percentage into its reduced fraction and equivalent decimal (e.g. 12.5% → 1/8).Cholesky decomposition calculatorFactor a symmetric positive-definite matrix A into L·Lᵀ, where L is lower triangular — the Cholesky decomposition. Enter A on an editable square grid and it returns L, Lᵀ and the product L·Lᵀ; if the matrix is not symmetric or not positive-definite, it tells you which condition failed. Twice as fast as LU, Cholesky is used in optimization, Kalman filters and Monte-Carlo simulation.QR decomposition calculatorFactor a matrix A into Q·R, where Q has orthonormal columns and R is upper triangular, using the modified Gram-Schmidt process. Enter A on an editable grid (rows ≥ columns), and it returns Q, R and the product Q·R so you can check the factorization at a glance. QR is the workhorse behind least-squares regression and eigenvalue algorithms.

Open Partial Fraction Decomposition Calculator and you get an answer straight away, with no account to create. You will find it under Calculus, with Partial Derivative Calculator and LU Decomposition Calculator for the neighbouring cases.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Partial Fraction Decomposition Calculator do?

Breaks a rational function into simple fractions, covering distinct linear factors, repeated factors and irreducible quadratics. The setup and the linear system solved for the coefficients are both shown, since that is the part being learned.

When would I actually use this?

Checking a derivative or an integral you worked out by hand, finding where a function turns, and getting a numeric answer when no closed form exists.

What is the most common mistake?

Integrating across a discontinuity as if it were not there. A numeric method will happily return a finite value for an integral that diverges — check the domain before trusting the number.

How is Partial Fraction Decomposition Calculator different from Partial Derivative Calculator?

They sit next to each other but answer different questions: Partial Derivative Calculator is the one to open when you need it to compute partial and mixed derivatives of a multivariable function symbolically. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

LU Decomposition Calculator is the closest one after this: Factor a square matrix into a lower L and upper U triangular matrix (Doolittle method).

What else is worth having open alongside it?

Fraction Calculator and Continued fraction calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

Symbolic results are exact; numeric ones come from adaptive quadrature or a standard step method, and the tool reports which. Where both are available, compare them — a large gap means the problem is ill-conditioned.

Further reading

All guides →
How-toHow to Convert a Percentage to a Fraction: Over 100, Then ReduceA percentage is just a fraction out of 100. Put the number over 100, reduce to lowest terms, and handle decimal percentages like 12.5% by clearing the decimal first. With examples.How-toHow to Multiply and Divide Fractions: Multiply Across, Flip to DivideMultiplying fractions needs no common denominator — just multiply across. Dividing means multiplying by the reciprocal. Learn both with worked examples and how to simplify.How-toHow to Add and Subtract Fractions: Common Denominator, Combine, SimplifyYou can only add or subtract fractions that share a denominator. Learn to find a common denominator, combine the numerators, and simplify the result, with a worked example.How-toHow to Convert a Fraction to a DecimalDivide the top number by the bottom. Here's the rule, why some fractions repeat, how to round them, and how to turn the result into a percentage.How-toHow to Round Numbers: Round Half Up, Round Half to Even, and MoreRound to any decimal place or number of significant figures, and learn when to use round half up versus round half to even to avoid bias.How-toHow to Find Prime Factors: Factor Trees and the Division MethodBreak any whole number into its prime building blocks with a factor tree or repeated division — and write the result as a clean prime factorization with exponents.