8.1.2 Multiplying and Dividing Rational Expressions (continued) Example 2 Simplifying by Factoring − 1 Recall that addition is commutative. Therefore, binomial factors such as ( x + a ) and ( a + x ) are common factors because x + a = a + x for all values of a and x . Subtraction is not commutative. Therefore, binomial factors such as ( x − a ) and ( a − x ) are not common factors. However, factoring − 1 from one of the binomials produces common factors. x − a = − 1( − x + a ) = − 1( a − x ) Typically, − 1 is factored from the binomial in the numerator. A graphing calculator can be used to identify the x -values for which a rational expression is undefined. 1. Enter the original expression as Y1. 2. Enter the simplified expression as Y2 3.View the table. 4. Identify the x -vales for which Y1 or Y2 show “ERROR”. These are the x -values that make the rational expression undefined.
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