Simplifying a complicated fraction with variables and weird stuff -_- help plz?

Question

Simplify the expression. its a huge fraction so plz bear with me.

((30x^2)/(x+2)) (divided by) (15x^3-30x^2)/(x^2-4)

if u cant understand that, ill type it out in words...

in parentheses, 30"x" squared over "x" plus 2, (end) plus 2"x" over "x" squared (end)(end parentheses) divided by 15"x"cubed minus 30 "x" squared over "x"squared minus 4, yea....i dont understand how to get the answer, im having problems with the reducing, plugging in a number for x doesnt help either, i tried distributing, the 30x^2/x+2 times the right side of the equation and the 2x/x^2 times the right side again; i get 2/1 on one side and a mess on the other...eh i mite skip it

Answer 1

(30xx)//(x+2) // (15xxx-30xx)//(xx-4)

When you have a fraction over a fraction, you flip and multiply.

(30xx)(xx-4) // (x+2)(15xxx-30xx)

Lets do some factoring... difference of squares on xx-4 and GCF on 15xxx-30xx

(30xx)(x+2)(x-2) // (x+2)(15xx)(x-2)

(x+2) and (x-2) on both sides cancel

(30xx) // (15xx)

Factor out 15xx.

Answer:  2

Answer 2

Confucious say: huge fraction sometimes disguises simple solution.   The key to this thingamijig is that if you have:  A/B  divided by C/D, "flipping" the second fraction to its reciprocal converts the whole mess to a multiplication or

AD/BC.  So if you set it up that way, you see wonderous reductions, like (x^2-4)/(x+2), which becomes (if you remembered stuff from before  [(x+2)(x-2)]/x+2 or  just plain old (x-2).   Try the other part for a big surprise.  

Answer 3

Ok, first let me right it out mathematically just so you know exactly what problem I think you are trying to get across (based on your algebraic description, not your text one):

    30*x^2

    ----------

      x+2

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

15*x^3 - 30*x^2

   -----------

    x^2 - 4

1.  Start by simplifying it into one numerator and one denominator

                  30*x^2 * (x^2 - 4)

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

            (x + 2) * (15*x^3 - 30*x^2)

2.  Multiply out the denominator

                (numerator)

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

15*x^4 - 30*x^3 + 30*x^3 - 60*x^2

3.  If you notice, 30*x^3 cancels and you can also cancel out a 15x^2 from the numerator and the denominator.  This leaves you with:

           2*(x^2 - 4)

         -------------------   =   2

              x^2 - 4

Answer 4

Notice the

  Simplify;   X²-4 = (X-2)(X+2)

15X³-30X² = 15X²(X-2)

= 30X²      (X-2)(X+2)

   ......  *    .........          ***The X-2 and X+2 cancel out by division

   (X+2)     15X²(X-2)        numerator and denominator.

=30X²/15X²

=2