Rational Expressions — Core Skills

The core idea, one worked example, and short practice.

Written and reviewed by the Study Mondo Education TeamLast updated August 21, 2026

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Rational Expressions: The Basics

A rational expression is a fraction with letters in it, like $\frac{3x + 12}{x + 4}$ . Two rules run this whole topic.

First, the bottom can never be zero. Any value of $x$ that makes the denominator zero is undefined and gets thrown out. To find it, set the bottom equal to zero and solve.

Second, you may cancel factors, not terms. A factor is something being multiplied. A term is something being added. So factor the top, factor the bottom, then cancel anything that matches. For $\frac{3x + 12}{x + 4}$ , the top factors into $3(x + 4)$ , the $(x + 4)$ cancels, and the answer is $3$ .

You cannot cross out the $x$ letters in $\frac{x + 4}{x + 6}$ . Those are terms, not factors, so that fraction is already as simple as it gets.

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The core idea, one worked example, and short practice.

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