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Math Help - Algebraic Fraction

  1. #1
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    Algebraic Fraction

    1 / x + x + 1 / x - x


    I am unsure as to how this is done. Any help is greatly appreciated.

    Thank you.
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  2. #2
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    Quote Originally Posted by stellina_91 View Post
    1 / x + x + 1 / x - x


    I am unsure as to how this is done. Any help is greatly appreciated.

    Thank you.
    Is it 1 / (x + x) + 1 / x - x or (1 / x) + x + 1 / x - x?

    And what do you want to do with it. Integrate? Differentiate? Put under a common denominator? Paint red?
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  3. #3
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    The first one please, I would like to simplify it.
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  4. #4
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    Quote Originally Posted by stellina_91 View Post
    The first one please, I would like to simplify it.
    \frac{1}{x^2 + x} + \frac{1}{x^2 - x} = \frac{1}{x(x + 1)} + \frac{1}{x(x - 1)}

    so you should try to put over a common denominator of x(x+1)(x-1):

    = \frac{x - 1}{x(x + 1)(x-1)} + \frac{x+1}{x(x - 1)(x+1)}

    = \frac{(x - 1) + (x + 1)}{x(x + 1)(x-1)}

    = \frac{2x}{x(x + 1)(x-1)}

    = \frac{2}{(x + 1)(x-1)}, \, x \neq 0

    = \frac{2}{x^2 - 1}.

    You can check this by plugging in a value or two of x and seeing that you get the same answer for each expression.
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  5. #5
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    Thanks so much for your help! I understand completely
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