Simplifying Rational Expressions and Stating Domain
Restrictions
Vocabulary:
 A rational expression is an expression that can be written as a ratio of two polynomials.
 It is in simplest form if the numerator and denominator have no factors in common other
than 1.
 The domain of an algebraic expression is the set of real numbers that the variable is
permitted to have. A rational expression is undefined when the denominator is zero.
Steps to simplify rational expressions.
1. Factor the numerator and denominator.
2. Find the restrictions for the denominator.
3. Simplify if possible.
Simplify the following. State any domain restrictions.
8
x
a.
b.
2x
3x 2  9x
d.
g.
x 2  5x  4
x 2  16
27x 3  8
6x 2  x  2
e.
h.
x3 x
x 2  5x  6
x 3  x 2  4x  4
3x 3  x 2  10x
c.
f.
8
x 2  4x  12
x2 1
x2  x 2