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Math Help - Looking for options equal to the equation

  1. #1
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    Looking for options equal to the equation

    I have an equation;

    3 + 6x - x^3 / 3x^2

    I am thinking;

    multiply both sides by 3x^2

    3x^2 (3 + 6x - x^3)

    Divide both sides by 3;

    = 1 / x^2 + 6x - x^3, which leaves;

    = 1 / x^2 + 6x - x^2

    or am I completely off the mark?

    Thanks

    David
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  2. #2
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    Re: Looking for options equal to the equation

    Uhm... I see just one side >.>

    Anyway, the first thing you should do is: 3x^2 \neq  0 \Rightarrow  x \neq 0.

    If you multiply 3 + 6x - x^3 / 3x^2 by 3x^2, you obtain 3+60-x^3, not 3x^2 (3 + 6x - x^3).
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  3. #3
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    Re: Looking for options equal to the equation

    It seems that I have the wrong idea to this type of problem, where I am looking for an equation which is EQUIVALENT to the one written.

    3 + 6x - x^3 / 3x^2

    so an equivalent could be;

    9x - x^3 / 3x^2

    I thought that there would be a way of working out equivalent equations but not sure of the correct method?
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  4. #4
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    Re: Looking for options equal to the equation

    \frac{a}{b} and \frac{c}{d} are equivalent if and only if \frac{a}{b}= \frac{c}{d}.

    Do you want to find x such as \frac{3 + 6x - x^3}{3x^2}=\frac{9x-x^3}{3x^2}?
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  5. #5
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    Re: Looking for options equal to the equation

    Quote Originally Posted by veileen View Post
    \frac{a}{b} and \frac{c}{d} are equivalent if and only if \frac{a}{b}= \frac{c}{d}.

    Do you want to find x such as \frac{3 + 6x - x^3}{3x^2}=\frac{9x-x^3}{3x^2}?
    Yes I think your right, I am asked to find equivalent equations to the question above, I think now that what I am suppose to do is trial and error with the solutions I am given by putting values into both the question and solutions, then if they balance, i.e. LIKE = LIKE, then the equations selected for answers should be right.

    I will work my way through some examples and keep you upto date with my progress.

    Thank you so far for your help

    Regards

    David
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Looking for options equal to the equation

    If that's the equation then it's quite easy because the denominators are equal that means the numerators also has to be equal therefore you have to solve:
    3+6x-x^3=9x-x^3

    Note that x\neq 0
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  7. #7
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    Re: Looking for options equal to the equation

    Quote Originally Posted by Siron View Post
    If that's the equation then it's quite easy because the denominators are equal that means the numerators also has to be equal therefore you have to solve:
    3+6x-x^3=9x-x^3

    Note that x\neq 0
    A problem is only easy to solve if one knows how to solve it, where at this time I don't
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  8. #8
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    Re: Looking for options equal to the equation

    Quote Originally Posted by David Green View Post
    I have an equation;

    3 + 6x - x^3 / 3x^2

    I am thinking;

    multiply both sides by 3x^2

    3x^2 (3 + 6x - x^3)

    Divide both sides by 3;

    = 1 / x^2 + 6x - x^3, which leaves;

    = 1 / x^2 + 6x - x^2

    or am I completely off the mark?

    Thanks

    David
    First off, what you have posted is a rational expression, not an equation. Equations have an equal sign. As posted, there is nothing to "solve".

    It would be a good idea for you to post any given directions so that someone can provide the guidance you seek.
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  9. #9
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    Re: Looking for options equal to the equation

    Quote Originally Posted by skeeter View Post
    First off, what you have posted is a rational expression, not an equation. Equations have an equal sign. As posted, there is nothing to "solve".

    It would be a good idea for you to post any given directions so that someone can provide the guidance you seek.
    OK I shall start again.

    Choose the TWO options that are EQUIVALENT to;

    3 + 6x - x^3 / 3x^2

    I thought these were equivalent;

    1/x^2 + 6x - x^2

    and

    9x - x^3 / 3x^2

    Other examples given;

    (1) 1 + 5x

    (2) 1 + 6/x - x/3

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

    (4) 2/x + 1/x^2 - x/3

    (5) 1 + 2x/x^2 - x/3

    (6) 3 + 6x^2 / 3x^2

    I tried putting numbers into the original expression and working out a solution, then using the same numbers in the example expressions to try and get the same answers, however I couldn't get the same answers, so there is obviously something there I am not understanding correctly?

    Any help much appreciated.

    Regards

    David
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  10. #10
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    Re: Looking for options equal to the equation

    Quote Originally Posted by David Green View Post
    OK I shall start again.

    Choose the TWO options that are EQUIVALENT to;

    3 + 6x - x^3 / 3x^2

    I thought these were equivalent;

    1/x^2 + 6x - x^2 no

    and

    9x - x^3 / 3x^2 no

    ... examples given;

    (1) 1 + 5x

    (2) 1 + 6/x - x/3

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

    (4) 2/x + 1/x^2 - x/3

    (5) 1 + 2x/x^2 - x/3

    (6) 3 + 6x^2 / 3x^2
    Lesson 1 : what you originally posted , 3 + 6x - x^3 / 3x^2 , could be interpreted as ...

    3 + 6x - \frac{x^3}{3x^2}

    or

    3 + 6x - \frac{x^3}{3} \cdot x^2

    ... if one strictly adheres to the order of operations.

    To avoid any confusion on behalf of your reader, type the expression using parentheses around the numerator and denominator ...

    (3 + 6x - x^3) / (3x^2)

    ... now there is no doubt what you mean.

    Lesson 2:

    \frac{3 + 6x - x^3}{3x^2} = \frac{3}{3x^2} + \frac{6x}{3x^2} - \frac{x^3}{3x^2} = \frac{1}{x^2} + \frac{2}{x} - \frac{x}{3}

    looks to me that only expression (4) is equivalent, unless you did not use parentheses in expression (5) , and you really meant

    (1 + 2x)/x^2 - x/3

    \frac{1+2x}{x^2} - \frac{x}{3}
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