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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.
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