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# Simplifying Complex Fractions

Recall that a fraction can be written using the division symbol, Ã·.

For example:

â€¢ can be written 2 Ã· 3.

â€¢ can be written (4x + 15) Ã· (x + 8).

â€¢ can be written

The expression, , is called a complex fraction.

A complex fraction is a fraction that contains other fractions.

Here are some examples of complex fractions:

To simplify a complex fraction we first write it as a division problem.

Then we follow the procedure for dividing rational expressions.

Procedure â€” To Simplify a Complex Fraction

Step 1 Write the complex fraction using a division symbol, Ã·.

Step 2 Invert the second fraction and change the division symbol, , to the multiplication symbol, Â·.

Step 3 Factor the numerators and denominators.

Step 4 Cancel all pairs of factors common to the numerators and denominators.

Step 5 Multiply the numerators. Multiply the denominators.