Rational Expressions
Review:
Simplify the following fractions:
%
#!
#)
)
'$
%&!
**The ability to factor the numerator and the denominator of
a fraction is a very important part of working with fractions**
Definition:
A rational expression is any expression that can be written as a
polynomial divided by a polynomial.
Examples:
B$  #B#  B
B$  #B#  "
#B  "
B#  $
"
$
$
B#
B#  #B  "
**When working with a rational expression it is important to
recognize that the expression cannot be evaluated at any values
that cause division by zero. We recognize such values as
restricted values and we make a statement in a problem that
such values are not allowed**
Examples:
Determine the restricted values for each expression.
$
3B  #
$B  #
B#  %
#B
B#  %
**To simplify (reduce) a rational expression, factor the
numerator and denominator; then divide the numerator and
denominator by common factors. Make sure to recognize that
the simplified form is only equal to the original form for values
that do not cause division by zero**
Simplify the following rational expressions:
$ B# C$
") B C%
B#
B#  "
 %B  &
=#  #=
%  #=
%B#  "'B  )
%B#  "'B  "#
(B#  &
(B#  &
Why can't we simplify a rational expression by dividing
common terms from the numerator and denominator of
a fraction?
#$
#&
B#  "
B#  %
is this the same as
is this the same as
&
$
"
%
?
?