Divide the following rational expressions?

Question

x-2

-----------

4x

------------

x^2-4x+4

--------------

12x

a) 3

-------

x-2

b) 1

----------

3(x-2)

c) 1

----------

3(x+2)

d) 2

---------------

x+2

Answer 1

x-2

--------

4x

--------

x^2-4x+4

-----------

12x

=x-2           12x     (when division changes multiply

-------     x  --------    reciprocal takes place)

4x             x^2-4x+4

=x-2              12x

-------       x  ---------  

4x                (x-2)(x-2)

=3

-----( cancel x-2 )

(x-2)

The answer is a)