College Algebra / Unit 2 Alg 106 worked example, 60 to 90 seconds
Simplifying a Rational Expression
The idea
Simplifying a rational expression means factoring the numerator and the denominator completely, then canceling the factors they share.
In practice
Simplify (x² − 9)/(x² + 5x + 6). Factor both floors: the numerator is a difference of squares, (x − 3)(x + 3); the denominator's pair hunt gives (x + 2)(x + 3). The shared factor (x + 3) cancels: (x − 3)/(x + 2). Spot-check with a number: at x = 1, the original is −8/12 = −2/3 and the simplified form is −2/3 — the same value in a smaller dress. Factoring first is not optional: cancellation reads factors only, and unfactored floors show none. A different number works as well as x = 1 for the spot-check; any value that keeps both denominators alive settles agreement.
Where people slip
Cancel whole factors, never terms inside them.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
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