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ALGEBRA / RATIONAL EXPRESSIONS

Rational Expression Calculator for Simplifying and Combining Algebraic Fractions with Steps

Updated By Unit Conversion Plus

Simplify or combine polynomial fractions and retain the restrictions created by their original denominators.

Enter one or two expressions

Expression A
Expression B

Enter coefficients from highest power to constant. For x² − 1, enter 1, 0, −1.

What is a rational expression?

A rational expression is a quotient of two polynomials. It is defined only where its denominator is nonzero. A factor may cancel algebraically, but a value excluded by the original denominator remains excluded from the simplified expression.

Combining polynomial fractions

Addition and subtraction use a common denominator. Multiplication combines numerators and denominators directly. Division multiplies by the reciprocal, which also requires the second expression’s numerator to be nonzero.

Numerical coefficient results

The calculator uses polynomial Euclidean division to identify common factors. Small floating-point residues are removed, but coefficients that are not close to simple values may be displayed as decimals.

Frequently asked questions

Does cancelling a factor remove an excluded value?

No. Restrictions come from the original expression, so a value that made an original denominator zero stays excluded.

Why do addition and subtraction create a larger denominator?

The expressions must first be rewritten over a common denominator before their numerators can be combined.