TABLE OF CONTENTS In a mathematical sense, a rational expression is defined as a quotient of two polynomials. In this section we discuss the rational expression structure of an algebraic expression and describe an algorithm that transforms an expression to a particular rational form.
Definition 6.46 (Mathematical Definition) Let S={ x 1, , x m} be a set of generalized variables. An algebraic expression u is a general ratio nal expression (GRE) in S if it has the form u= p/ q, where p and q are GPEs in S.
For each example, we have given one possible choice for S. Notice that the definition is interpreted in a broad sense to include GPEs for which the denominator is understood to be 1.
The Numerator and Denominator Operators. To determine if an expression is a GRE, we must define precisely the numerator and denominator of the expression. The Numerator and Denominator operators, which are used for this purpose, are defined by the following transformation rules.
Definition 6.48 Let u be an algebraic expression.
ND-1. If u is a fraction, then
ND-2. Suppose u is a power. If the exponent of u is a negative integer or a negative fraction, then
otherwise
ND-3. Suppose u is a product and v=Operand( u, 1). Then
ND-4. If u does not satisfy any of the previous rules, then
Consider the expression 
. Then
The Numerator
