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 Dependent Variable

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# Adding and Subtracting Rational Expressions with Different Denominators

To add or subtract rational expressions with different denominators, we must build up each rational expression to equivalent forms with identical denominators. Of course, it is most efficient to use the LCD as in the following examples.

Example 1

Different denominators

Perform the indicated operations.

Solution

a) The LCD for a2b and ab3 is a2b3. To build up each denominator to a2b3, multiply the numerator and denominator of the first expression by b2, and multiply the numerator and denominator of the second expression by a:

 Build up each denominator to the LCD. Add the numerators.
 Build up each denominator to the LCD 12. Distributive property Subtract the numerators. Note that 6x - 9 is put in parentheses. Remove the parentheses. Combine like terms.

Caution

Before you add or subtract rational expressions, they must be written with identical denominators. For multiplication and division it is not necessary to have identical denominators.

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