ADDING AND SUBTRACTING RATIONAL EXPRESSIONS
ADDING AND SUBTRACTING RATIONAL EXPRESSIONSADDING AND SUBTRACTING RATIONAL EXPRESSIONS
ADDING AND SUBTRACTING RATIONAL EXPRESSIONS
To
To To
To
Add or Subtract Two Fractions
Add or Subtract Two FractionsAdd or Subtract Two Fractions
Add or Subtract Two Fractions
Example 1
Example 1Example 1
Example 1 a)
a) a)
a) Add
&
'(
)
*
'(
b)
b) b)
b) Subtract
+
,
-
'
,
Solution: a)
a) a)
a)
&
'(
)
*
'(
/
& 0 *
'(
/
'+
'(
b)
b)b)
b)
+
,
-
'
,
/
+ 1 '
,
/
2
,
The same principles apply when adding
addingadding
adding or subtracting rational expressions
subtracting rational expressionssubtracting rational expressions
subtracting rational expressions containing
variables.
To
To To
To
Add or Subtract Rational Expressions with a Common Denominator
Add or Subtract Rational Expressions with a Common DenominatorAdd or Subtract Rational Expressions with a Common Denominator
Add or Subtract Rational Expressions with a Common Denominator
1.
Add or subtract the numerators
.
2.
Place
the sum or difference of the numerators found in step 1 over
the common denominator
.
3.
Simplify the faction if possible
.
Example 2
Example 2Example 2
Example 2 Add
(
; 1 +
)
; 0 <
; 1 +
Solution:
(
; 1 +
)
; 0 <
; 1 +
/
( 0=;0<)
; 1 +
/
; 0 *
; 1 +
Example
Example Example
Example 3
33
3 Add
;
>
0?;1<
=;0+)=;1<)
)
2;0'<
=;0+)=;1<)
Solution:
;
>
0?;1<
=;0+)=;1<)
)
2;0'<
=;0+)=;1<)
/
@;
>
0?;1<A0 =2;0'<)
=;0+)=;1<)
Write as a single fraction.
Remove parentheses
/
;
>
0?;1< 0 2;0'<
=;0+)=;1<)
in the numerator.
/
;
>
0&;0'C
=;0+)=;1<)
Combine like terms.
/
=;0+)=;0<)
=;0+)=;1<)
Factor.
/
=;0+)=;0<)
=;0+)=;1<)
/
=;0<)
=;1<)
Divide out common factors.
When subtracting rational expressions, n
When subtracting rational expressions, nWhen subtracting rational expressions, n
When subtracting rational expressions, note that the
ote that theote that the
ote that the
entire numerator of the second fraction
entire numerator of the second fractionentire numerator of the second fraction
entire numerator of the second fraction
=not just the first term) must be subtracted.
must be subtracted.must be subtracted.
must be subtracted. Also note that the sign of
each
term of the
numerator being subtracted will change when the parentheses are removed.
Example
Example Example
Example 4
44
4 Subtract
;
>
1<;0?
;
>
0&;0'<
-
;
>
1 2;1+
;
>
0&;0'<
H
I
)
J
I
/
H
)
J
I
,
I
K
0
H
I
-
J
I
/
H
-
J
I
,
I
K
0
