What this calculator does
This tool decomposes a proper rational expression of the form (ax + b) / [(x − r₁)(x − r₂)], where the denominator has two distinct real roots, into the sum of two simple fractions: A/(x − r₁) + B/(x − r₂).
The method: the cover-up method
The constants are found with the standard cover-up (Heaviside) technique: A = (a·r₁ + b) / (r₁ − r₂) and B = (a·r₂ + b) / (r₂ − r₁). The calculator also recombines A and B at a test value of x and compares it back against the original expression as a quick sanity check.
- The two roots must be different real numbers; a repeated root requires a different decomposition form (A/(x−r) + B/(x−r)²) not covered by this simple tool.
- Provided for general educational purposes.
Last reviewed August 2026