Cambridge International Mathematics

350 Algebraic fractions (Chapter 16)

2 Write as a single fraction:

a

2

x+1

+

3

x¡ 2

b

5

x+1

+

7

x+2

c

5

x¡ 1

¡

4

x+2

d

2

x+2

¡

4

2 x+1

e

3

x¡ 1

+

4

x+4

f

7

1 ¡x

¡

8

x+2

g

1

x+1

+

3

x

h

5

x

¡

2

x+3

i

x

x+2

+

3

x¡ 4

j 2+

4

x¡ 3

k

3 x

x+2

¡ 1 l

x

x+3

+

x¡ 1

x+2

m

2

2 x¡ 1

¡

1

x+3

n

7

x

¡

4

3 x¡ 1

o

x

x+2

¡

x+1

x¡ 2

p

2

x(x+1)

+

1

x+1

q

1

x¡ 1

¡

1

x

+

1

x+1

r

2

x+1

¡

1

x¡ 1

+

3

x+2

s

x

x¡ 1

¡

1

x

+

x

x+1

3 Simplify:

a

3 x¡ 9

6

£

12

x^2 ¡ 9

b

5 x¡ 20

2 x

¥

2 x¡ 8

x

c

2 x+8

5

£

10

x^2 ¡ 16

d

e

x^2 +x¡ 2

x^2 ¡ 4

£

x^2 +3x¡ 10

x^2 +7x+10

f

x^2 ¡ 4

x^2 +3x

¥

x^2 +7x+10

x^2 +8x+15

gh

4 x^2 ¡ 9

x^2 +4x¡ 5

¥

2 x^2 ¡ 3 x

x^2 +5x

4 Answer theOpening Problemon page 339.

PROPERTIES OF ALGEBRAIC FRACTIONS

Writing expressions as a single fraction can help us to find when the expression is zero.

However, we need to be careful when we cancel common factors, as we can sometimes lose values when

an expression is undefined.

Example 15 Self Tutor

Write as a single fraction: a

3

(x+ 2)(x¡1)

+

x

x¡ 1

b

¡ 3

(x+ 2)(x¡1)

+

x

x¡ 1

a

3

(x+ 2)(x¡1)

+

x

x¡ 1

=

3

(x+ 2)(x¡1)

+

³ x

x¡ 1

́μx+2

x+2

¶

fLCD=(x+ 2)(x¡1)g

=

3+x(x+2)

(x+ 2)(x¡1)

=

x^2 +2x+3

(x+ 2)(x¡1)

which we cannot simplify further.

x^2 ¡x¡ 2

x+1

¥

x¡ 2

5

2 x^2 ¡x¡ 3

6 x^2 +x¡ 15

£

4 x^2 ¡ 7 x+3

4 x^2 +x¡ 3

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Y:\HAESE\IGCSE01\IG01_16\350IGCSE01_16.CDR Tuesday, 7 October 2008 2:02:55 PM PETER