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 x^{2}  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
. 