Cambridge International Mathematics

352 Algebraic fractions (Chapter 16)

3 Write as a single fraction:

a

2 x

3

+

3 x

5

b

2 x

3

£

3 x

5

c

2 x

3

¥

3 x

5

d

2 x

3

¡

3 x

5

4 Simplify by factorisation:

a

4 x+8

x+2

b

5 ¡ 10 x

2 x¡ 1

c

4 x^2 +6x

2 x+3

5 Write as a single fraction:

a

x+3

4

+

2 x¡ 2

3

b

x¡ 1

7

¡

1 ¡ 2 x

2

c

2

x+2

+

1

x

6 Simplify by factorisation:

a

8 ¡ 2 x

x^2 ¡ 16

b

x^2 +7x+12

x^2 +4x

c

2 x^2 ¡ 3 x¡ 2

3 x^2 ¡ 4 x¡ 4

7aWrite

2 x

x+3

¡

12

(x+ 1)(x+3)

as a single fraction.

b Hence, find the values ofxwhen this expression is: i undefined ii zero.

Review set 16B

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1 Simplify:

a

4 a

6 a

b

x

3

£ 6 c 3 ¥

1

n

d

12 x^2

6 x

2 Simplify, if possible:

a

3 x+15

5

b

3 x+15

3

c

2(a+4)

(a+4)^2

d

abc

2 ac(b¡a)

3 Write as a single fraction:

a

3 x

4

+2x b

3 x

4

¡ 2 x c

3 x

4

£ 2 x d

3 x

4

¥ 2 x

4 Simplify by factorisation:

a

3 ¡x

x¡ 3

b

5 x+10

2 x+4

c

3 x^2 ¡ 9 x

ax¡ 3 a

5 Write as a single fraction:

a

x

5

+

2 x¡ 1

3

b

x

6

¡

1+2x

2

c

3

2 x

¡

1

x+2

6 Simplify by factorisation:

a

2 x^2 ¡ 8

x+2

b

x^2 ¡ 5 x¡ 14

x^2 ¡ 4

c

3 x^2 ¡ 5 x¡ 2

4 x^2 ¡ 7 x¡ 2

7aWrite

24

x^2 ¡ 4

¡

3 x

x+2

as a single fraction.

b Hence, find the values ofxwhen this expression is: i undefined ii zero.

8 Simplify: a

3 x+7

x¡ 1 ¡^13

x¡ 2

b

2 x^2 +5x+2

x^2 ¡ 4

¥

2 x^2 +x

x^2 +x¡ 6

.

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y:\HAESE\IGCSE01\IG01_16\352IGCSE01_16.CDR Thursday, 2 October 2008 2:13:40 PM PETER