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Math Help - Simplifying and finding the domain

  1. #1
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    Simplifying and finding the domain

    So i transferred schools and i was in algebra 2 last year, now im in precal and the school is a lot more difficult and there are some things i havent covered.

    Can u give me the steps on how u did it?because if i dont learn anything itll be useless

    how do i find the domain of 4x^3+3 when x greater than or equal to 0, and the domain of x+1 over 2x+1

    also how do i simplify this? 4(3-x) / x-3

    and another x+13/x^3(3-x) * x(x-3)/5

    can i simplify this? x^2-36/6-x im at (x+6)(x+6)/6-x can i simplify it any further?

    last one: simplify the complex fraction x-4 / x/4-4/x (writing it down on paper would make it more clear with the / as fraction)
    -thanks
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  2. #2
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    You made need to use some brackets so these problems make a bit more sense.

    \displaystyle \frac{x^2-36}{6-x}=\frac{(x+6)(x-6)}{6-x}\neq \frac{(x+6)(x+6)}{6-x}
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  3. #3
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    Simplify: 4(3-x) / x-3
    (I don't know if this is correct or not)

    Suppose that it is an equation, with an equals:

    y=\dfrac{4(3-x)}{x-3}

    -1 * y=-1 * \dfrac{4(3-x)}{x-3}

    -1y=\dfrac{4(x-3)}{x-3}

    -1y=4

    y=-4


    \dfrac{4(3-x)}{x-3} = -4, x\ne{3}

    It has lost some data when it is simplified to -4, because x cannot be 3.


    Is the second simplify question:

    \dfrac{x+13}{x^3(3-x)} * \dfrac{x(x-3)}{5} ?

    And the forth one:

    \dfrac{x-4}{\frac{x}{4}-\frac{4}{x}} ?
    Last edited by Educated; September 7th 2010 at 01:04 AM. Reason: Asked about the other questions
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  4. #4
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    (3-x) = -(x-3)

    \Rightarrow \dfrac{4(3-x)}{x-3} = \dfrac{-4(x-3)}{x-3} = -4.

    how do i find the domain of 4x^3+3 when x greater than or equal to 0, and the domain of x+1 over 2x+1
    I find this confusing. Do you mean the range?
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  5. #5
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    Quote Originally Posted by TheCoffeeMachine View Post
    (3-x) = -(x-3)

    \Rightarrow \dfrac{4(3-x)}{x-3} = \dfrac{-4(x-3)}{x-3} = -4.

    I find this confusing. Do you mean the range?
    my friend said the problem was already done, so maybe its the books problem.

    Quote Originally Posted by Educated View Post
    Simplify: 4(3-x) / x-3
    (I don't know if this is correct or not)

    Suppose that it is an equation, with an equals:

    y=\dfrac{4(3-x)}{x-3}

    -1 * y=-1 * \dfrac{4(3-x)}{x-3}

    -1y=\dfrac{4(x-3)}{x-3}

    -1y=4

    y=-4


    \dfrac{4(3-x)}{x-3} = -4, x\ne{3}

    It has lost some data when it is simplified to -4, because x cannot be 3.


    Is the second simplify question:

    \dfrac{x+13}{x^3(3-x)} * \dfrac{x(x-3)}{5} ?

    And the forth one:

    \dfrac{x-4}{\frac{x}{4}-\frac{4}{x}} ?
    yes for the second, and yes to the 4th

    thanks for answering guys
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