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Simplifying Complex Fractions

Example

Simplify:

Solution

Step 1 Write the numerator and denominator each as a single fraction.
The LCD of the numerator is x.
Multiply 5 by .
Write as a single fraction.
The LCD of the denominator is 4x2.
Multiply 2 by
Write as a single fraction.
So, we now have
Step 2 Rewrite the fraction using ÷.
Step 3 Invert the second fraction and change ÷ to ·.
Step 4 Multiply.
Factor and cancel the common factor of x.
Multiply.

Thus, the result is .