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9.5: Addition, Subtraction, and
Complex FractionsObjectives: Students will be able to…• Add and subtract rational
expressions• Simplify complex fractions
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To add or subtract rational expressions you need a common denominator!!!
O Example:1.
2.
xx 2
7
2
3
xx
2
2
4
Common Denominator…so just subtract numerators
4
6
4
3
xx
x
4
63
x
x
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You Try…Add or subtract
5
52
5
x
x
x
x
5
5:
x
xAnswer
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When you have unlike denominators, find the Least Common Denominator (LCD) of the rational expression. (May need to factor denominators first!!)
O Rewrite each expression using the LCDO We do this with regular fractions LCD = 6
2
1
3
2
6
1
6
3
6
43
3
2
1
2
2
3
2
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Now, lets do it with rational expressions:
Factor denominators:
233 363
4
xx
x
x
1233
423
xx
x
xThis one needs a 2x +1 This one needs another
x
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Subtract. 9
1
96
122
xxx
x
Factor Denominators:
)3)(3(
1
)3)(3(
1
xxxx
x
Needs an (x-3)Needs another (x+3)
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You Try: Perform the indicated operation
4
1
23
2.)2
11
12.)1
x
x
x
x
x
x
x
x
1
1:
x
xAnswer
)4)(23(
275:
2
xx
xxAnswer
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Add or subtract.
934
122
x
x
xx
x
)1)(3)(3(
35:
xxx
xAnswer
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Complex FractionsO A fraction within a fraction!!O Contains a fraction in numerator or
denominator
Example:
13
41
43
xx
x
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It is against the law to have a fraction within a fraction, so lets simplify:
13
41
43
xx
x
METHOD 1: Add expressions in denominator:
Multiply by reciprocal, and simplify:
114
33
114
)1)(4(
4
3
x
x
x
xx
x
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Method 2: Multiply numerator and denominator by LCD of both (don’t forget
to distribute)
13
41
43
xx
x
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Simplify:
xx
x1
1412
15
2:
xx
Answer