Adding & Subtracting Rational Expressions - Metropolitan Community College
ADDING AND SUBTRACTING RATIONAL EXPRESSIONS
To Add or Subtract Two Fractions
H J H)J
) /
, IK0
I
I
I
Example 1
&
a) Add
'(
&
Solution: a)
'(
*
)
)
H J H-J
- /
, IK0
I
I
I
b) Subtract
'(
*
'(
/
&0*
'(
/
'+
b)
'(
+
,
-
'
,
/
+
-
'
+1'
/
,
,
,
2
,
The same principles apply when adding or subtracting rational expressions containing
variables.
To 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
Add
Solution:
Example 3
Add
Solution:
(
;1+
(
;1+
;0<
) ;1+
)
;0<
;1+
; > 0?;1<
=;0+)=;1 0?;1<
=;0+)=;1 1 2;1+
; > 0&;0'<
Solution:
; > 1 0&;0'<
-
; > 1 2;1+
; > 0&;0'<
/
=; > 1 1 2;1+)
; > 0&;0'<
/
; > 1 02;0+
; > 0&;0'<
0&;0'<
/
28Q < X ? . To do this, we multiply the fraction on the left by &R > and the fraction on the
right by
+
2; > R
)
(;
R V
/
?+R > 0 (;
R V
or
(; 0 ?+R >
R V
and the second fraction by
1 ?;1 ................
................
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