Cambridge International Mathematics

348 Algebraic fractions (Chapter 16)

3 Simplify:

a

x

3

+2 b

m

2

¡ 1 c

a

3

+a d

b

5

¡ 2

e

x

6

¡ 3 f 3+

x

4

g 5 ¡

x

6

h 2+

3

x

i 6 ¡

3

x

j b+

3

b

k

5

x

+x l

y

6

¡ 2 y

4 Simplify:

a

x

3

+

3 x

5

b

3 x

5

¡

2 x

7

c

5

a

+

1

2 a

d

6

y

¡

3

4 y

e

3

b

+

4

c

f

5

4 a

¡

6

b

g

x

10

+3 h 4 ¡

x

3

Addition and subtraction of more complicated algebraic fractions can be made relatively straightforward if

we adopt a consistent approach.

For example:

x+2

3

+

5 ¡ 2 x

2

=

2

2

μ

x+2

3

¶

+

3

3

μ

5 ¡ 2 x

2

¶

fachieves LCD of 6 g

=

2(x+2)

6

+

3(5¡ 2 x)

6

fsimplify each fractiong

We can then write the expression as a single fraction and simplify the numerator.

Example 12 Self Tutor

Write as a single fraction: a

x

12

+

x¡ 1

4

b

x¡ 1

3

¡

x+2

7

a

x

12

+

x¡ 1

4

=

x

12

+

3

3

μ

x¡ 1

4

¶

=

x+3(x¡1)

12

=

x+3x¡ 3

12

=

4 x¡ 3

12

b

x¡ 1

3

¡

x+2

7

=

7

7

μ

x¡ 1

3

¶

¡

3

3

μ

x+2

7

¶

=

7(x¡1)

21

¡

3(x+2)

21

=

7(x¡1)¡3(x+2)

21

=

7 x¡ 7 ¡ 3 x¡ 6

21

=

4 x¡ 13

21

D MORE COMPLICATED FRACTIONS [2.9]

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y:\HAESE\IGCSE01\IG01_16\348IGCSE01_16.CDR Thursday, 2 October 2008 1:57:07 PM PETER