Let’s consider this example
Therefore the expression is undefined at x= 7 and x = -4
Example 1 (Bittinger & Ellenbogen, 2006)
A rational expression is said to be
when the numerator and the denominator
have no factors (other than 1) in common.
To simplify a rational expression, we first factor the numerator and denominator. We
then identify factors common to the numerator and denominator, rewrite the expression
as a product of two rational expressions (one of which is equal to 1), and then remove
the factor equal to 1.
Canceling is a shortcut that can be used—and easily
—to simplify rational
expressions. Canceling must be done with care and understanding. Essentially,
canceling streamlines the process of removing a factor equal to 1.
Working with rational expressions is exactly the same as working with fractions. All the
same rules are in play.
The Product of Two Rational Expressions
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