In this Section:
In this section, we will introduce the rational expression. We begin with the definition for a rational number. A rational number is any number that can be formed as the quotient of two integers (with a non-zero denominator). Similarly, a rational expression is the quotient of two polynomials (with a non-zero denominator). Recall that we can never divide by zero and if we see division by zero, that expression is considered “undefined”. Since there is a denominator involved with a rational expression, we are concerned with where the rational expression is undefined. This simply means we are finding values for the variable that make the denominator zero. Any value that does this is considered a restricted value. The next scenario we deal with is how to simplify a rational expression. We perform this operation by factoring the numerator and denominator completely, then canceling any common factors.