Cambridge International Mathematics

Algebraic fractions (Chapter 16) 351

b

¡ 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)

=

(x+ 3)(x¡1)

(x+ 2)(x¡1)

=

x+3

x+2

EXERCISE 16D.2

1 Write as a single fraction:

a

2

x(x+1)

+

1

x+1

b

2

x(x+1)

+

x

x+1

c

2 x

x¡ 3

+

4

(x+ 2)(x¡3)

d

2 x

x¡ 3

¡

30

(x+ 2)(x¡3)

e

3

(x¡2)(x+3)

+

x

x+3

f

x

x+3

¡

15

(x¡2)(x+3)

g

2 x

x+4

¡

40

(x¡1)(x+4)

h

x+5

x¡ 2

¡

63

(x¡2)(x+7)

2aWrite

2

(x+ 2)(x¡3)

+

2 x

x¡ 3

as a single fraction.

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

3 Simplify: a

x

x¡ 2 ¡^3

x¡ 3

b

3 x

x+4¡^1

x¡ 2

c

x^2

x+2¡^1

x+1

d

x^2

2 ¡x+9

x¡ 3

e

1

x^2 ¡

1

4

x¡ 2

f

x¡ 3

x^2 ¡

1

16

x¡ 4

4aSimplify:

2

x+1¡

x

3

2 ¡x

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

Review set 16A

#endboxedheading

1 Simplify:

a

6 x^2

2 x

b 6 £

n

2

c

x

2

¥ 3 d

8 x

(2x)^2

2 Simplify, if possible:

a

8

4(c+3)

b

3 x+8

4

c

4 x+8

4

d

x(x+1)

3(x+ 1)(x+2)

The expression is zero when

. The expression is
undefined when
and also when We
can see this from the
original expression.

x

x

x:

=3

=2

=1

¡

¡

1

1

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y:\HAESE\IGCSE01\IG01_16\351IGCSE01_16.CDR Thursday, 2 October 2008 2:12:39 PM PETER