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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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