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Math Help - STEPS to Solve simple equation

  1. #1
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    STEPS to Solve simple equation

    I have an equation and answer but do not know the steps involved to arrive at the answer. Try as I might I do need help!!

    1 / x = x / 1 + x

    Solving for x

    x = (1+ sqrt. {5}) / 2

    Is it a linear equation?
    Last edited by neilthomason; September 13th 2010 at 08:18 AM. Reason: display wrong
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  2. #2
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    Quote Originally Posted by neilthomason View Post
    I have an equation and answer but do not know the steps involved to arrive at the answer. Try as I might I do need help!!

    1 / x = x / 1 + x

    Solving for x

    x = (1+ sqrt. {5}) / 2

    Is it a linear equation?
    Please learn order of operations and parentheses.

    "1 / x = x / 1 + x" means "1 / x = (x / 1) + x" which I'm quite sure isn't what you meant.

    \dfrac{1}{x}=\dfrac{x}{1+x}

    cross multiply and you get a quadratic.
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  3. #3
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    Thanks you are quite correct I did not mean this, I am looking for your definition (Image) of the equation.

    A man once said that we are all ignorant.......... but not about the same things.

    What will the quadratic look like?
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  4. #4
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    Quote Originally Posted by neilthomason View Post
    What will the quadratic look like?
    It will look like this.

    Golden ratio - Wikipedia, the free encyclopedia
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  5. #5
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    Quote Originally Posted by neilthomason View Post
    Thanks you are quite correct I did not mean this, I am looking for your definition (Image) of the equation.

    A man once said that we are all ignorant.......... but not about the same things.

    What will the quadratic look like?
    First of all we know that x \neq 0, -1

    Second, multiply each side by the others denominator: \dfrac{1}{x} \cdot \dfrac{1+x}{1+x} = \dfrac{x}{1+x} \cdot \dfrac{x}{x} (we can do this because of what I defined above)

    When we simplify we get: \dfrac{1+x}{x(1+x)} = \dfrac{x^2}{x(1+x)}

    The denominators are the same and hence will cancel to give 1+x = x^2 - put into standard form and use the quadratic formula to solve
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