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Partial Fractions Decomposer with Steps

Turn any rational function P(x)/Q(x) into H(x) plus a proper partial fraction expansion. We run long division, find complex roots, group them into linear or irreducible quadratic factors, solve the coefficient system, and show every step along the way.

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Set P(x) and Q(x)

Input polynomials

Examples: "2x^3 - 5x + 1" or coefficients "1, 0, -5, 1" (descending degree).

Examples

    Result

    Quotient H(x)
    --
    Proper part
    --

    Factor terms and coefficients

    Factor Power Term Coefficients

    How it is calculated

      FAQ

      Can it handle repeated and quadratic factors?

      Yes. The solver clusters complex roots into real linear and irreducible quadratic factors, allocates the right number of unknowns for every power, and solves them in one Gaussian sweep.

      How do I export or share the decomposition?

      Use Copy LaTeX for typesetting, Export CSV for a structured table, and Share to copy a URL with your current inputs so classmates and students can review the same breakdown.