Rational Expression Simplifier
Add, subtract, multiply or divide two rational expressions (fractions of polynomials).
Inputs
Coefficients highest to lowest, e.g. '1,2' for x+2
e.g. '1,-1' for x−1
Result Numerator
2x^2 - 3x + 1
Result Denominator
1x^2 - 2x + 1
Step by step
Values used
Numerator 1 coefficients = 1,2; Denominator 1 coefficients = 1,-1; Operation = Add (+); Numerator 2 coefficients = 1,-3; Denominator 2 coefficients = 1,-1
Addition
a/b + c/d = (a·d + c·b) / (b·d)
Multiplication
a/b × c/d = (a·c) / (b·d)
Result Numerator
= 2x^2 - 3x + 1
Result Denominator
= 1x^2 - 2x + 1
How it works
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
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.