2.2 Algebraic Fractions

Copyright © 2010 McGraw-Hill Australia. Permission is granted to reproduce for classroom use.

CHAPTER 2 ALGEBRA AND SURDS

Use the rule above to simplify the algebraic fractions below 1.

maths in focusMathematics and Extension 1

Year 11

RULE 1

To simplify algebraic fractions factorise fi rst, then cancel common factors

(a) b3

3 12+

(b) xx x23 2

-

(c) y

y

16

2 82-

-

(d) x x

x6

22- -

+

(e) a a

a2 8

42

2

- -

-

(f) x

x x4 16

122

-

- -

(g) x

x y x

27

4 3 33-

- + -] ]g g

(h) x

x x8 1

2 7 43

2

+

- -

RULE 2

To add and subtract algebraic fractions make the lowest common denominator

2. Use the rule above to simplify

(a) a a2

33

++

(b) x x3

24

3+-

-

(c) x x5

2 13

4-+

+

(d) a a8

3 52

2 1+-

-

(e) x x9

63

32-

-+

(f) x x x2

54

32

22+

--

+-

ch2.indd 8ch2.indd 8 9/11/09 12:13:33 PM9/11/09 12:13:33 PM

Copyright © 2010 Cengage Learning Australia. Permission is granted to reproduce for classroom use.

2.2 Algebraic Fractions (Cont.)

Copyright © 2010 McGraw-Hill Australia. Permission is granted to reproduce for classroom use.

CHAPTER 2 ALGEBRA AND SURDS

3. Use the rules above to simplify

maths in focusMathematics and Extension 1

Year 11

RULE 3A

To multiply algebraic fractions factorise fi rst then cancel any common factors

RULE 3B

To divide by an algebraic fraction, multiply by its reciprocal. Then proceed as for multiplication

(a) 2 8

163 12

4x

xx

x x2 2

#+

-

-

+

(b) a aab b

ab

55 25

2525

2 2

2

'-

-

-

(c) x x x

x xx

x4 16 4

126 18

42

2

#- + -

- -

+

(d) x x

xx xx x

4 48

24 8

2

3

2

2

'- +

-

-

-

(e) x x

xx xx

26 18

227

2 3 2

3

'+ -

-

+

-

(f) 4 64

2 4 165 10

8 16x

x xx

x x2

2 2

#-

+ -

-

- +

ch2.indd 9ch2.indd 9 9/11/09 12:13:36 PM9/11/09 12:13:36 PM

Copyright © 2010 Cengage Learning Australia. Permission is granted to reproduce for classroom use.