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Simplifying Complex Fractions
Simplifying Complex Fractions
Here is a method for simplifying complex fractions.
Procedure
To Simplify a Complex Fraction
Step 1 Find the LCD of the fractions contained in the complex
fraction.
Step 2 Multiply the numerator and denominator of the complex
fraction by the LCD.
Step 3 Simplify.
Example
Simplify:
| Solution |
|
| Step 1
Find the LCD of the fractions contained in the complex fraction. |
| Factor x2 - 5x. |
 |
| The LCD is x(x - 5). |
|
| Step 2 Multiply the numerator and
denominator of the complex
fraction by the LCD. |
 |
| Step 3 Simplify. |
|
| Distribute x(x - 5) in the
denominator. |
 |
| Cancel pairs of common factors
in the numerator and in the
denominator.
|
= |
| Simplify. |
 |
So, the result is
 .
Note:
We are multiplying both the
numerator and denominator by the
same number, x(x - 5). This means that we are multiplying
the complex fraction by 1 in the
form
 .
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