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Note:

Notice that

Here, a and b are real numbers and a ≠ b.

Example 1

Reduce to lowest terms:

Solution

For the numerator, find two numbers whose product is -27 and whose sum is 6. These numbers are -3 and 9.

The denominator is the difference of two squares: 3^{2} - x^{2}.

Thus,

The answer may be written in several ways.