1
L1
§ 1.1 Real numbers and their properties
Expressions of the form
a
b
.
We will be dealing with fractional expressions on a
regular basis. Here are two important questions:
1. When is the fractional expression undefined
?
Answer
: When the denominator
0
b
=
(division by 0
is undefined).
Note: As more situations arise, there will be more
restrictions such as when taking square roots.
2. When is the fractional expression equal to zero
?
Answer
: When the numerator
0
a
=
, provided the
denominator
0
b
≠
.
A word of caution
:
0
0
is not a number!
Therefore, a number that makes an expression equal to
0
0
does not
make it equal to 0.
2
Example
.
a)
Find the value of
x
so that
2
3
4
x
x
−
+
is undefined.
b) Find the value of
x
so that
2
0
3
4
x
x
−
=
+
.
Example
.
a)
Find the value of
x
so that
(
3)
x x
x
−
is undefined.
b) Find the value(s) of
x
so that
(
3)
0
x x
x
−
=
.
Note
:
In this example we could cancel out the
x
’s to
get just
(
3)
x
−
, but we still have the restriction:
0
x
≠
.
This will be discussed in detail in sections 1.5 and 4.5.

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