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Math Help - Simplifying help

  1. #1
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    Simplifying help

    x^3-3x^2+3x-9 / x^4-81

    i cant seem to get this answer right
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  2. #2
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    assuming your function is ??

     \frac{x^3-3x^2+3x-9}{ x^4-81}

    You need to factor both the numerator and denominator to determine any cancelling expressions.

    Then the denominator will factor as follows x^4-81 = (x^2)^2-9^2 = (x^2+9)(x^2-9) = (x^2+9)(x-3)(x+3)

    This can be further factored using complex numbers. Is this a requirement?

    Do you know the factor theorem? You will need it to factor the numerator. Try to find f(a) = 0 where a is an integer factor of 9.
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  3. #3
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    thanks,

    I got that far but how am i supposed to factor the numerator and how am i allowed to cancel out?
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  4. #4
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    \frac{x^3-3x^2+3x-9}{x^4-81} = \frac{x^3-3x^2+3x-9}{(x^2+9)(x^2-9)} = \frac{x^3-3x^2+3x-9}{(x^2+9)(x+3)(x-3)}

    This is just using the difference of squares method on the denominator, which is that {a^2-b^2} = (a+b)(a-b)

    \frac{x^2(x-3)+3(x-3)}{(x^2+9)(x+3)(x-3)} = \frac{(x^2+3)(x-3)}{(x^2+9)(x+3)(x-3)} = \frac{(x^2+3)}{(x^2+9)(x+3)}

    This is just using that {ax+ay}={a(x+y)}. You see how both {x^3-3x^2} can be divided by {x^2} and likewise {3x-9} can be divided by 3? Apply that rule again on {x^2(x-3)+3(x-3)}, where (x-3) is the a and x^2 and 3 are the x and y respectively. Then, I just divided both sides of the fraction by (x-3).
    Last edited by Lord Voldemort; September 25th 2009 at 03:02 PM.
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  5. #5
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    Quote Originally Posted by samtheman17 View Post
    thanks,

    I got that far but how am i supposed to factor the numerator and how am i allowed to cancel out?

    The numerato you can factor by grouping. If you group x^3 and -3x^2 together and 3x and -9 together. You take the common factor from each and get

    x^2(x-3) + 3(x-3)

    then by the laws of grouping you can put them together and get (x^2 + 3)(x-3) and in the denominator you have (x-3)(x+3)(x^2 + 9) and then you can cross out the (x-3) on the top and bottom and you're left with:

    (x^2 + 3)
    __________
    (x+3)(x^2 + 9)
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  6. #6
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    thank you,

    that helps so much
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