A rational number is a number which can be written as a fraction. The root word is ratio.
Definition (Rational Expression)
A rational expression is a fraction in which both the top and the bottom are polynomials.
Procedure: (Determining the Numbers for which a Rational Expression is Undefined)
Set the denominator equal to zero and solve. Any solutions to this equation are numbers that make the rational expression undefined (since you would then be dividing by zero).
Procedure: (Simplifying a Rational Expression)
1. Factor the top and bottom of the rational expression completely.
2. Cancel any common factors between the top and the bottom.
IMPORTANT: You MUST determine for what numbers the expression is undefined BEFORE you reduce the expression to lowest terms.
Simplify. For expressions with only one variable, determine for what numbers the expression is undefined.
DO NOT CANCEL PIECES OF THE SUMS! YOU MUST FACTORE BEFORE YOU BEGIN CANCELLING!
Watch out for factors that are opposites of one another. If you follow my earlier advice and always factor out a negative number if the leading coefficient is negative, then you should have no real problems with this.