ACT Preparation / Unit 8 ACT 0721 worked example, 60 to 90 seconds
Simplifying a Complex Fraction
The idea
A complex fraction has fractions within its numerator or denominator. To simplify it, work in three steps. First, find the least common denominator of every small fraction inside it. Second, multiply the top and the bottom of the large fraction by that LCD, which clears the small fractions. Third, simplify the result, and factor to cancel what you can.
In practice
Worked example: (1 + 1/x) ÷ (1 − 1/x²). Step one: the LCD is x². Step two: the top becomes x² + x and the bottom x² − 1. Step three: x(x + 1)/((x + 1)(x − 1)) = x/(x − 1).
Where people slip
Multiply every term of the top and of the bottom by the LCD, including whole-number terms such as 1. Missing one leaves a fraction behind and a wrong answer.
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