Partial Fraction Calculator
Split 1/(px+q)(rx+s) into A and B terms
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Working out how to split 1/(px+q)(rx+s) into A and B terms is easier with Partial Fraction Calculator, which answers as you type. Drop p (first factor px+q), q and r (second factor rx+s) into Partial Fraction — the figure refreshes as you type. Nothing in Partial Fraction is a black box. Anyone comparing options in Math can use Partial Fraction to compare scenarios. Partial Fraction runs in your browser. Math data stays in the tab. Looking for partial fraction decomposition calculator algebra rational expression or free online partial fraction calculator? Partial Fraction covers both. Keep Partial Fraction bookmarked for next time. Open Partial Fraction and enter your numbers.
What does the Partial Fraction Calculator do?
Partial Fraction Calculator works out the split 1/(px+q)(rx+s) from the p, q, and r, using Math conventions. With the defaults, partial fraction calculator gives a result of A = 0.5, B = 0.5.
- Inputs: p, q, and r.
- Output: the split 1/(px+q)(rx+s), together with the chain that produced it.
- Method: the standard Math equation, fed by p, q, and r and solved locally.
Quick answer
partial fraction calculator returns a result of A = 0.5, B = 0.5 with the default inputs (p of 1, q of -1, r of 1).
How does the Partial Fraction Calculator work?
Partial Fraction Calculator computes the split 1/(px+q)(rx+s) directly from your inputs — the p, q, and r feed the formula. The split 1/(px+q)(rx+s) comes from local arithmetic, and the inputs never travel anywhere.
How it works
What separates Partial Fraction Calculator from a bare number is the trail behind it: p, q, and r go in, the split 1/(px+q)(rx+s) comes out, and the route between the two stays on screen.
How to use it
- p — read first by partial fraction, so an error here reaches the result untouched.
- q — consumed at the top of the partial fraction chain; later steps refine but never correct it.
- r — entered on partial fraction as a plain number in the labelled unit — nothing converted behind it.
- Check the result on Partial Fraction Calculator: the split 1/(px+q)(rx+s) is shown as soon as the inputs are valid, and the steps beneath it show exactly how it was derived.
- Explore Partial Fraction Calculator: each input change recalculates instantly, and watching the split 1/(px+q)(rx+s) move tells you which factor dominates your case.
The formula behind the result
Where the Math definition splits into stages, Partial Fraction Calculator keeps the stages separate so each one can be checked before the split 1/(px+q)(rx+s) is accepted.
Worked example: with p of 1, q of -1, r of 1, this partial fraction calculation returns A = 0.5, B = 0.5. The same run reports Result: 0.5/(1x+-1) + 0.5/(1x+1) | Check: combine back over the common denominator.
The steps it follows:
- Write A/(px+q) + B/(rx+s) = 1/((px+q)(rx+s))
- Multiply both sides by the denominator: A(rx+s) + B(px+q) = 1
- Match coefficients — solve the 2x2 system
- A = s/(ps−qr) = 0.5000, B = −q/(ps−qr) = 0.5000
Understanding the result
Quote the output from Partial Fraction Calculator with the case attached, because the same figure means different things under different p, q, and r.
Where it helps
Reach for Partial Fraction Calculator when the task is budgeting for the next few months, comparing a new quote with an old one, and spot-checking a quoted figure and an estimate from memory will not survive a second look.
Common mistakes
Trusting a figure copied from a spreadsheet without re-entering it is how unit mismatches enter Partial Fraction Calculator unnoticed.
Tip: Partial Fraction Calculator returns A = 0.5, B = 0.5 at its defaults; double the p (first factor px+q) and it returns A = 0.3333, B = 0.3333.
Assumptions and limitations
Results from Partial Fraction Calculator are estimates computed from the values entered; real-world outcomes can differ when fees, taxes, or conditions not modeled here apply.
Why use this calculator
Because the figure is recalculated rather than remembered, Partial Fraction Calculator never hands you a stale figure left behind by someone else.
Frequently Asked Questions
Which figure does partial fraction calculator produce?
Feeding p, q, and r into Partial Fraction Calculator produces the figure along with a written record of every operation that got there. Because the same figure can be recalculated offline, Partial Fraction Calculator keeps working where a connection-dependent tool would stop.
What calculation does the page perform?
The first steps are write a/(px+q) + b/(rx+s) = 1/((px+q)(rx+s)), then multiply both sides by the denominator: a(rx+s) + b(px+q) = 1. Partial Fraction Calculator treats the formula as a sequence rather than a black box — every operator is printed with the values it consumed on the way to the split 1/(px+q)(rx+s).
Which fields does the Partial Fraction Calculator need?
Partial Fraction Calculator asks for p, q, and r and nothing more.
If the p (first factor px+q) doubles, what follows?
At the defaults Partial Fraction Calculator returns A = 0.5, B = 0.5; doubling p (first factor px+q) to 2 moves it to A = 0.3333, B = 0.3333.
How should the the Partial Fraction Calculator result be read?
The main number the partial fraction calculator returns is the split 1/(px+q)(rx+s) for your exact inputs. Partial Fraction Calculator assumes the units shown in each label — entering values in different units will skew the split 1/(px+q)(rx+s) proportionally.
When would someone reach for the page?
Common ground for Partial Fraction Calculator: budgeting for the next few months, comparing a new quote with an old one, and spot-checking a quoted figure, and any moment when a result needs to be explained rather than announced. If the split 1/(px+q)(rx+s) surprises you, change nothing and re-read the labels first; a unit mismatch is far more common than a wrong formula.
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