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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
.