Cambridge International Mathematics

346 Algebraic fractions (Chapter 16)

The rules for addition and subtraction of algebraic fractions are identical to those used with numerical

fractions.

To add two or more fractions we obtain the lowest common

denominatorand then add the resulting numerators.

a

c

+

b

c

=

a+b

c

To subtracttwo or more fractions we obtain thelowest common

denominatorand then subtract the resulting numerators.

a

c

¡

d

c

=

a¡d

c

To find the lowest common denominator, we look for thelowest common multiple of the denominators.

For example: when adding^34 +^23 , the lowest common denominator is 12 ,

when adding^23 +^16 , the lowest common denominator is 6.

The same method is used when there are variables in the denominator.

For example: when adding

4

x

+

5

y

, the lowest common denominator isxy,

when adding

4

x

+

3

2 x

, the lowest common denominator is 2 x,

when adding

1

3 a

+

2

5 b

, the lowest common denominator is 15 ab.

To find

x

2

+

3 x

5

we notice the LCD is 10. We then proceed in the same manner as for ordinary fractions:

x

2

+

3 x

5

=

x

2 £ 5

+

3 x£ 2

5 £ 2

=

5 x

10

+

6 x

10

=

11 x

10

Example 9 Self Tutor

Simplify: a

x

3

+

5 x

6

b

3 b

4

¡

2 b

3

a

x

3

+

5 x

6

=

x

3 £ 2

+

5 x

6

fLCD =6g

=

2 x

6

+

5 x

6

=

2 x+5x

6

=

7 x

6

b

3 b

4

¡

2 b

3

=

3 b£ 3

4 £ 3

¡

2 b£ 4

3 £ 4

fLCD =12g

=

9 b

12

¡

8 b

12

=

b

12

ADDING AND SUBTRACTING

ALGEBRAIC FRACTIONS [2.9]

C

£ 5

£ 2

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y:\HAESE\IGCSE01\IG01_16\346IGCSE01_16.CDR Thursday, 2 October 2008 1:53:10 PM PETER