Need help with complex rational expression problem?

Question

x-2/12x

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

x^2-4/4x

how you solved it would help alot

Answer 1

All you are doing is dividing fractions. Multiply by the reciprocal.

(x-2)/12x * 4x/(x^2-4)

(x-2)/[3(4x)]  *  4x/[(x-2)(x+2)]  "cancel" up & down or diagonally

1/[3(x+2)]

Answer 2

x-2    x^2-4

-------/----------------

12x       4x

x-2      4x

-------*----------------

12x  (x-2)(x+2)

4x=1  12x=3

2  x-2's cancel

          1

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

3 (x+2)=3x+6

Answer 3

=-2/11x

Answer 4

    x-2

   ------

   12x

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

  x^2-4

  -------

   4x

factoring out 4x in the denominators of the expression above and below

and factoring out x^2-4

   x-2

   ------

  4x(3)

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

(x-2)(x+2)

  -------

   4x

canceling x-2 in the numerators and 4x in the denominators

    1

   ------

    3

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

  x + 2

  -------

    1

simplify...

      1

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

  3(x+2)

Answer 5

((x - 2) / (12x)) / ((x^2 - 4) / (4x)) = ((x - 2) / (12x)) * ((4x) / (x^2 - 4)), because dividing by a rational expression is the same as multiplying by its reciprocal.  4x / 12x reduces to 1/3, so now you have (1/3) * (x - 2) / (x^2 - 4).  You can factor (x^2 - 4) = (x + 2)(x - 2), so you can write this as (1/3) * (x - 2) / (x + 2)(x - 2).  (x - 2) cancels itself, so you have (1/3) / (x + 2) = 1 / (3x + 6).

Answer 6

I agree with the 1st and 2nd answer

(x-2)/12x

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

(x-2)(x+2)/4x

(x-2)/12x * 4x/(x-2)(x+2) <=== mult recip

1/3(x+2) <====After (x-2) and 4x cancel

1/(3x+6)