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  A2 Core

 Algebra and functions

Section 6: Algebraic fractions and division

Exercise

1.  Simplify

(i)5

52

−

−

 x 

 x  x   (ii)

)8)(2(

1662

−−

−+

 x  x 

 x  x  

(iii)2

22

)(   a x 

a x 

−

−  (iv)

v

v

26

3

−

− 

2.  Write as a single fraction in its simplest form

(i)33

28

43

2

−

×−+

 x 

 x  x 

  (ii)242124

23 2

2

−−

−−×

+   x  x 

 x  x 

 x  

3.  Write as a single fraction in its simplest form

(i)4

9

2

155 2 −÷

+   cc  (ii)

232

32

12 2

22

−−

−+÷

+

−

 x  x 

 x  x 

 x 

 x  x  

4.  Express as a single fraction

(i)5

3

2

 x  x +   (ii)

 x  x  4

1

3

2−  

5.  Express as a single fraction

(i)5

1

3

2

−

+

+   x  x 

  (ii)14

2

32

5

+

−

−   x  x 

 

(iii)13

5

−

−

t 

t   

6.  Express as a single fraction

(i))1(4

1

)5(2

1

+

−

+   x  x 

  (ii)uuu

u

−

+

+− 2

1

44

32

 

7.  Solve these equations:

(i) 764

3=−

 x  x   (ii) 13

12

27

52

30=

+

+

−   x  x 

 

8.  Divide

(i) 3 23 2 4 x x x − + −  by  x  + 2

(ii) 4 22 1 x x x + − −  by2 1 x    +  

(iii) 3 x   by

(iv) 6 x  – 2 by 2x + 3

(v) by

2 2 x    +

2

3 x    +12

2 1 x x − −  

© MEI, 23/08/05  1/1