
Rational Expressions and Their Simplification
A rational number is a fraction, like 2/5. A rational
expression is a ratio in
which the numerator and denominator may both be polynomials, like
EXAMPLE: Find all numbers for which each rational
expression is undefined.
The expression is undefined if the denominator is zero.
When is the
denominator zero?
EXAMPLE: Find all numbers for which each rational expression is undefined.
SIMPLIFYING RATIONAL EXPRESSIONS:
A rational expression can be simplified by dividing out
common factors
shared by its numerator and denominator. For example,
We can’t cancel common terms:
factors:
WRONG
We can cancel common
RIGHT
TO SIMPLIFY A RATIONAL EXPRESSION
1.) Factor the numerator and denominator
completely
2.) Divide out all the common factors 
EXAMPLE: Simplify
EXAMPLE: Simplify the following
EXAMPLE: Find the opposites of the following
How can you notice opposite pairs?
What is the ratio of two expressions that are opposite pairs?
EXAMPLE: Simplify
