What is this rational expression Simplified?

 ....6x^3

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

15x^4 - 60x^3

......6x^3

=----------------

...15x^3(x - 4)

......... 2

=-----------------

....5(x - 4)

 where x ≠ 4   undefined..

6x^3 / (15x^4 - 60x^3)

=  2x^3 / (5x^4 - 20x^3)  

= 2 / (5(x - 4)) 

I guess you mean 6x^3 / (15x^4 - 60x^3).  Right?

The expression is undefined if x = 0, and also undefined if x = 4.  Otherwise, you have

6/(15x - 60)

as a simpler form of the same expression.

As typed, the first term groups as [6(x^3)/15]x^4 = (2x^7) / 5; but a small voice tells me that's probably not what you meant.

If it was (6x^3) / (15x^4 - 60x^3), then start by noticing that the denominator factors as15x^3(x - 4).  That tells you the undefined values for the expression (where the denominator is zero) are x=0 and x=4.

That also helps you see the common factor of 3x^3 in the numerator and denominator, so the full expression simplifies to:

    2 / (5x - 20)

...which is still undefined at x=4, but not at x=0.  That means the reduced expression is equivalent to the original only for nonzero values of x.