EDGE Math 8

Domains of Rational Expressions

Definition

The domain of a rational expression is the set of all real numbers, except those that will make the denominator equal to zero.

When finding the domain of a rational expression, equate the denominator to zero, and then solve the resulting equation. The domain is the set of all real numbers, except the solutions to that equation, since these values will make the denominator of the rational expression equal to zero.

When the denominator of a rational expression consists of more than one factor, the Zero Product Principle can be applied to find the domain of a rational expression.

Zero Product Principle
If the product of two real numbers a and b is equal to 0, then at least one of the numbers is 0; that is, if $a b = 0,$ then either

a = 0, b = 0, or both .

For instance, if $(x - 1) (x - 2) = 0,$ then according to the Zero Product Principle, either

$x - 1 = 0$	or	$x - 2 = 0$
$x - 1$		$x - 2$