Rational Expression Simplifier
Add, subtract, multiply or divide two rational expressions (fractions of polynomials).
About Rational Expression Simplifier
Rational expressions are fractions whose numerator and denominator are polynomials. To add/subtract, find a common denominator (multiply the denominators). To multiply, multiply numerators and denominators. To divide, multiply by the reciprocal of the second fraction.
Formulas
Addition
a/b + c/d = (a·d + c·b) / (b·d)
- a
- Numerator 1
- b
- Denominator 1
- c
- Numerator 2
- d
- Denominator 2
Multiplication
a/b × c/d = (a·c) / (b·d)
- a
- Numerator 1
- b
- Denominator 1
- c
- Numerator 2
- d
- Denominator 2
Worked example
With the default values below, Rational Expression Simplifier returns Result Numerator of 2x^2 - 3x + 1. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Numerator 1 coefficients
- 1,2
- Denominator 1 coefficients
- 1,-1
- Operationone of Add (+), Subtract (−), Multiply (×), Divide (÷)
- Add (+)
- Numerator 2 coefficients
- 1,-3
- Denominator 2 coefficients
- 1,-1
Results
- Result Numerator
- 2x^2 - 3x + 1
- Result Denominator
- 1x^2 - 2x + 1
Step by step
- 1Values used
- 2Addition
- 3Multiplication
- 4Result Numerator= 2x^2 - 3x + 1
- 5Result Denominator= 1x^2 - 2x + 1
Assumptions and limits
- The result is derived only from the 5 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Does this cancel common factors?
The calculator performs the arithmetic correctly but does not always fully simplify the result by cancelling common polynomial factors.
How do I enter a constant?
Enter it as a single number coefficient, e.g. '5' for the polynomial 5, or '1,0,0' for x².