9.5: Addition, Subtraction, and

Complex FractionsObjectives: Students will be able to…• Add and subtract rational

expressions• Simplify complex fractions

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

You Try…Add or subtract

5

52

5

x

x

x

x

5

5:

x

xAnswer

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

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

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)

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

Add or subtract.

934

122

x

x

xx

x

)1)(3)(3(

35:

xxx

xAnswer

Complex FractionsO A fraction within a fraction!!O Contains a fraction in numerator or

denominator

Example:

13

41

43

xx

x

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

Method 2: Multiply numerator and denominator by LCD of both (don’t forget

to distribute)

13

41

43

xx

x

Simplify:

xx

x1

1412

15

2:

xx

Answer