Algebraic Fractions

1. Express 52

2

3

)23(7

)672(

3

x

x

xx

x

as a single fraction in its simplest form.(Total 4 marks)

2. Express )3)(1( xx

x+

9

122 x

x as a single fraction in its simplest form.

(Total 6 marks)

3. (a) Express as a fraction in its simplest form

214

13

3

22

xxx .

(3)

(b) Hence solve

1214

13

3

22

xxx .

(3)

4. Express as a single fraction in its simplest form

9

1582

2

x

xx × 2

2

)5(

62

x

xx.

(Total 4 marks)

5. f(x) = xx

xx

3

62

2

, x 0, x 3.

(a) Express f(x) in its simplest form.(3)

(b) Hence, or otherwise, find the exact solutions of f(x) = x + 1.(3)

(Total 6 marks)

Ashlawn School and Science college 1

6. (a) Simplify 1

232

2

x

xx

(3)

(b) Hence, or otherwise, express )1(

1

1

232

2

xxx

xx as a single fraction in its simplest

form.(3)

(Total 6 marks)

7. Express

2

6

)2()32(

322

2

xxxx

xx

as a single fraction in its simplest form.(Total 7 marks)

Ashlawn School and Science college 2