1Cademy - Rational Expression

Learn Before

Definition

Rational Expression

A rational expression is an expression written in the form $\frac{p}{q}$ , where $p$ and $q$ are polynomials and $q \neq 0$ . Just as a rational number is defined as the ratio of two integers with a nonzero denominator, a rational expression extends this idea by replacing integers with polynomials — it is the ratio of two polynomials whose denominator polynomial is not equal to zero. Because division by zero is undefined, the denominator must never be zero. Examples of rational expressions include $-\frac{24}{56}$ , $\frac{5x}{12y}$ , $\frac{4x+1}{x^2-9}$ , and $\frac{4x^2+3x-1}{2x-8}$ . Notice that $-\frac{24}{56}$ is simply a numerical fraction, yet it qualifies as a rational expression because a constant is a polynomial of degree zero — so the ratio of two constants is a ratio of two polynomials, provided the denominator is not zero. The same operations performed on numerical fractions — simplifying, adding, subtracting, multiplying, and dividing — are also performed on rational expressions.

Updated 2026-05-14

Contributors are:

Who are from:

References

Learn Before

Related

Learn After