Download your Word document
Two-Factor Partial Fraction Decomposition Calculator result sheet — free, supported by sponsors. Your download button appears in 20 seconds.
This free download is supported by sponsors — continuing in
20
Your file is generated in your browser when you choose Download — nothing is uploaded. If this calculator returns enough numeric data, the export also includes its best-fit chart alongside the readable table.
WorldCalculate result export
Two-Factor Partial Fraction Decomposition Calculator — result sheet
Decompose a rational expression with two distinct linear denominator factors and verify its value at a chosen x.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: (a x+b)/((x+p)(x+q))=A/(x+p)+B/(x+q); A=(b−a p)/(q−p); B=(a q−b)/(q−p).
This focused decomposition solves the two unknown numerators for a rational expression whose denominator is the product of two distinct linear factors. The page also evaluates the original and recomposed expressions at the selected x, making the algebraic identity checkable instead of returning only unexplained coefficients.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Numerator x coefficient a — minimum -1000000000; maximum 1000000000
- Numerator constant b — minimum -1000000000; maximum 1000000000
- First denominator offset p — minimum -1000000000; maximum 1000000000
- Second denominator offset q — minimum -1000000000; maximum 1000000000
- Check value x — minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Numerator x coefficient a | 5 |
| Numerator constant b | 7 |
| First denominator offset p | 1 |
| Second denominator offset q | 3 |
| Check value x | 2 |
A = 1; B = 4; original and recomposed values both equal 17/15 ≈ 1.133333333.
Assumptions and limits
- The denominator factors are distinct, so p and q cannot be equal.
- The evaluation point is not either denominator root: x must not equal −p or −q.
- The numerator and factors are real-valued and use one consistent algebraic variable x.
- The page handles exactly two distinct linear factors; repeated factors, irreducible quadratics, polynomial division, and symbolic simplification are outside this contract.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
No saved result was found. Please run the calculation first, then choose Download again.