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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Reducing Rational Expressions

## Reducing Rational Expressions of the Form

 Sometimes we need to simplify an expression such as the following: In the expression, notice that the numerator and denominator are the same except for the signs of the terms. To reduce the expression, we first factor -1 out of the numerator. Then we cancel common factors. = -1
The result is -1.

Note:

Notice that

Formula â€” To Simplify a Rational Expression of the Form

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

Example 1

Reduce to lowest terms:

Solution

 Step 1 Factor the numerator and denominator. 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: 32 - x2. Step 2 Cancel all pairs of factors common to the numerator and denominator. Since has the form it reduces to -1.

Thus,

Note:

The answer may be written in several ways.