math

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How to factor (x/x-2)-(x+2/x)
my answer is -x^2-x-2/x

and (3+sq rt 5)*(3-sq rt 5)
my answers are either 4 or 3*sq rt 5^2

are any of these right?

Thanks so much for all of your help.

  • math -

    I have a feeling your question is

    x/(x-2) - (x+2)/x

    Factoring doesn't make much sense, more than likely it says "simplify", am I right?

    for (3 + √5)(3 - √5)

    You should recognize the 'difference of squares' patter, or you could just expand it

    = 9 - 5 = 4

    4 is the only answer

  • math -

    Yes, you are right. It does say simplify.

  • math -

    back to x/(x-2) - (x+2)/x then

    common denominator is x(x-2)

    so x/(x-2) - (x+2)/x
    = [x^2 - (x+2)(x-2)] / [x(x-2)]
    = (x^2 - x^2 + 4)/[x(x-2)]
    = 4/(x(x-2))

  • math -

    I changed my answer to
    x/(x-2) - (x+2)/x to 4/x(x-2)

    Is that right?

  • math -

    got it, thanks!

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