1Cademy - Rational Equation

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Rational Expression

Definition

Rational Equation

A rational equation is an equation formed by connecting two rational expressions with an equal sign. Just as the general concept of an equation joins two algebraic expressions with the symbol $=$ , a rational equation does the same specifically with rational expressions. The presence of the equal sign is the critical feature that separates a rational equation from a rational expression: without it, the algebraic quantity is merely an expression rather than an equation.

For example, the following pairs illustrate the distinction:

$\frac{1}{8}x + \frac{1}{2}$ is a rational expression, but $\frac{1}{8}x + \frac{1}{2} = \frac{1}{4}$ is a rational equation.
$\frac{y + 6}{y^2 - 36}$ is a rational expression, but $\frac{y + 6}{y^2 - 36} = y + 1$ is a rational equation.
$\frac{1}{n - 3} + \frac{1}{n + 4}$ is a rational expression, but $\frac{1}{n - 3} + \frac{1}{n + 4} = \frac{15}{n^2 + n - 12}$ is a rational equation.

Updated 2026-05-01

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