How to multiply complex fractions - GRE Quantitative Reasoning

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Question

Simplify:

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Answer

Remember that fraction multiplication is the easiest of the arithmetical operations we can use on fractions. We can merely multiply the numerators and denominators by each other. As you will see, this is the easiest way to do this problem, for the numerators and denominators can be cancelled. Thus, we know:

Now, the parts of this fraction can be cancelled, giving us a much simpler expression:

, which is the same as

To simplify this, you just need to multiply the numerator by the reciprocal of the denominator; thus, we have:

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