Rational Expressions
R6_NOTES
MATH 1111
Section R.6
(p. 35-43)
Skills
Determine the domain of a
rational expression.
Simplify rational
expressions.
Multiply, divide, add, and
subtract rational
expressions.
Simplify complex rational
expressions.
Vocabulary
domain
equivalent expressions
least common denominator
(LCD)
A
rational expression
is the quotient of two polynomials.
The Domain of Rational Expressions
The domain of an algebraic expression is the set of all real numbers for which the
expression is defined.
Division by zero is not defined, so any number that makes the denominator 0 is
not in the domain of a rational expression.
Ex.
Find the domain of the following expressions.
Describe the domain using set-builder notation.
Simplifying, Multiplying, & Dividing Rational Expressions
To simplify rational expressions, we use the fact that
Ex.
Ex.
Equivalent expressions
have the same value for all numbers that are in both
domains.

NOTE: When multiplying or dividing rational expressions, it is usually best to factor each expression first.