Cambridge International Mathematics

Algebraic fractions (Chapter 16) 341

Example 2 Self Tutor

Simplify: a

(x+ 3)(x¡2)

4(x+3)

b

2(x+3)^2

x+3

a

(x+ 3)(x¡2)

4(x+3)

=

x¡ 2

4

b

2(x+3)^2

x+3

=

2(x+ 3)(x+3)

(x+3)

=2(x+3)

EXERCISE 16A.1

1 Simplify if possible:

a

6 a

3

b

10 b

5

c

3

6 x

d

8 t

t

e

t+2

t

f

8 a^2

4 a

g

2 b

4 b^2

h

2 x^2

x^2

i

4 a

12 a^3

j

4 x^2

8 x

k

t^2 +8

t

l

a^2 b

ab^2

m

a+b

a¡c

n

15 x^2 y^3

3 xy^4

o

8 abc^2

4 bc

p

(2a)^2

a

q

(2a)^2

4 a^2

r

(3a^2 )^2

3 a

s

(3a^2 )^2

9 a^2

t

(3a^2 )^2

18 a^3

2 Split the following expressions into two parts and simplify if possible.

For example,

x+9

x

=

x

x

+

9

x

=1+

9

x

:

a

x+3

3

b

4 a+1

2

c

a+b

c

d

a+2b

b

e

2 a+4

2

f

3 a+6b

3

g

4 m+8n

4

h

4 m+8n

2 m

3 Which of the expressions in 2 could be simplified and which could not? Explain why this is so.

4 Simplify:

a

3(x+2)

3

b

4(x¡1)

2

c

7(b+2)

14

d

2(n+5)

12

e

10

5(x+2)

f

15

5(3¡a)

g

6(x+2)

(x+2)

h

x¡ 4

2(x¡4)

i

2(x+2)

x(x+2)

j

x(x¡5)^2

3(x¡5)

k

(x+ 2)(x+3)

2(x+2)^2

l

(x+ 2)(x+5)

5(x+5)

m

(x+ 2)(x¡1)

(x¡1)(x+3)

n

(x+ 5)(2x¡1)

3(2x¡1)

o

(x+6)^2

3(x+6)

p

x^2 (x+2)

x(x+ 2)(x¡1)

q

(x+2)^2 (x+1)

4(x+2)

r

(x+2)^2 (x¡1)^2

(x¡1)^2 x^2

In these examples

is the

common factor.

(+3)x

1

(^11)
1
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y:\HAESE\IGCSE01\IG01_16\341IGCSE01_16.CDR Thursday, 2 October 2008 1:43:42 PM PETER