27
L4
§1.5 Rational Expressions
Definition
. A
rational expression
is the quotient of two
polynomials.
The
domain
of an expression is set of all real numbers,
for which the expression is defined.
For a rational expression
, the domain is the set of real
numbers that do not make the denominator equal to 0.
To find the domain of a rational expression
, first
determine all real values of
x
that make the
denominator equal to 0,
zeros of the denominator
.
Then, write:
Domain:
{
zeros of the denominator}
x
x
∈
≠
\
.
Reducing Rational Expressions:
Fundamental Principle of Fractions
:
ac
a
bc
b
=
(
0,
0)
b
c
≠
≠
Note: Assume restrictions on the variables when
writing a rational expression in lowest terms.
28
Example. Find the domain of each rational expression
and reduce it to the lowest terms.
Warning:
write the domain before canceling!
a)
2
3
x
x
x
−
Domain:
b)
2
5
10
3
5
2
x
x
x
−
=
−
−
Domain:
Multiplication and division
:
a
c
ac
b
d
bd
⋅
=
a
c
a
d
b
d
b
c
÷
=
⋅
(
0
0
0)
b
c
d
≠
≠
≠

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