Cambridge International Mathematics

344 Algebraic fractions (Chapter 16)

4 Simplify:

a

x^2 ¡x

x^2 ¡ 1

b

x^2 +2x+1

x^2 +3x+2

c

x^2 ¡ 4 x+4

2 x^2 ¡ 4 x

d

x^2 +4x+3

x^2 +5x+4

e

x^2 ¡ 4

x^2 ¡ 3 x¡ 10

f

x^2 +7x+12

2 x^2 +6x

g

x^2 +4x¡ 5

2 x^2 +6x¡ 20

h

x^2 +6x+9

x^2 +3x

i

2 x^2 ¡ 7 x¡ 4

x^2 ¡ 2 x¡ 8

j

3 x^2 +5x¡ 2

3 x^2 ¡ 4 x+1

k

2 x^2 ¡ 3 x¡ 20

x^2 ¡x¡ 12

l

8 x^2 +14x+3

2 x^2 ¡x¡ 6

The rules for multiplying and dividing algebraic fractions are identical to those used with numerical fractions.

These are:

Tomultiplytwo or more fractions, we multiply the numerators to

form the new numerator, and we multiply the denominators to form

the new denominator.

Todivideby a fraction we multiply by its reciprocal.

a

b

£

c

d

=

a£c

b£d

=

ac

bd

a

b

¥

c

d

=

a

b

£

d

c

=

ad

bc

MULTIPLICATION

Step 1: Multiply numerators and multiply denominators.

Step 2: Separate the factors.

Step 3: Cancel any common factors.

Step 4: Write in simplest form.

For example,

n^2

3

£

6

n

=

n^2 £ 6

3 £n

fStep 1g

=

n£n£ 2 £ 3

3 £n

fSteps 2 and 3g

=

2 n

1

=2n fStep 4g

Example 7 Self Tutor

Simplify: a

4

d

£

d

8

b

5

g

£g^3

a

4

d

£

d

8

=

4 £d

d£ 8

=^12

b

5

g

£g^3 =

5

g

£

g^3

1

=

5 £g£g£g

g

=5g^2

MULTIPLYING AND DIVIDING

ALGEBRAIC FRACTIONS [2.9]

B

11

11

2

1

1

1

1

1

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Y:\HAESE\IGCSE01\IG01_16\344IGCSE01_16.CDR Tuesday, 7 October 2008 2:02:02 PM PETER