ACT Preparation / Unit 8 ACT 0717 worked example, 60 to 90 seconds
Simplifying a Rational Expression
The idea
A rational expression is simplified in four steps. First, factor the numerator and the denominator completely. Second, record the excluded values: every value that makes the original denominator zero. Third, cancel each factor that appears in both. Fourth, write what remains, noting the excluded values beside it.
In practice
Worked example: simplify (x² + 2x − 15)/(x² − 9). Step one: the numerator is (x + 5)(x − 3) and the denominator (x + 3)(x − 3). Step two: x cannot be 3 or −3. Step three: cancel x − 3. Step four: (x + 5)/(x + 3), for x not equal to 3 or −3.
Where people slip
Watch for factors that are negatives of each other: (3 − x)/(x − 3) is −1, because 3 − x = −(x − 3).
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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