What is this rational expression Simplified?

6x^3 / 15x^4 - 60x^3 

and what values of x make it undefined? 

I get the basic idea but I can't seem to get the correct answer

4 Answers

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  • 2 months ago

     ....6x^3

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

    15x^4 - 60x^3

    ......6x^3

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

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

    ......... 2

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

    ....5(x - 4)

     where x ≠ 4   undefined..

  • 2 months ago

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

    =  2x^3 / (5x^4 - 20x^3)  

    = 2 / (5(x - 4)) 

  • ?
    Lv 7
    2 months ago

    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.

  • 2 months ago

    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.

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