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Multiplying and Dividing Rational Expressions
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Simplest Form of Rational Expressions

Example

Simplify p − 3 15 − 5 p .


Solution

First, factor the denominator.

p − 3 15 − 5 p = p − 3 5 ( 3 − p )

It may appear that the numerator and the denominator do not have a common factor. However, they actually have a common factor. Note that p−3=−( 3−p ) and, in general, a−b=−( b−a ). Hence,

p − 3 5 ( 3 − p ) = − ( 3 − p ) 5 ( 3 − p ) = − 1 5

Thus, the simplest form of p − 3 15 − 5 p is − 1 5 .