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Math Help - Help? i dont get it

  1. #1
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    Help? i dont get it

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

    I have the answer

    6-4x/(x-1)(x-1)

    but i dont understand how to get there
    anyhelp is greatly appreciated

    thank you
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  2. #2
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    Quote Originally Posted by madmatt View Post
    4/1 - x + 2/(1 - x)^2

    I have the answer

    6-4x/(x-1)(x-1)

    but i dont understand how to get there
    anyhelp is greatly appreciated

    thank you
    \frac{4}{1 - x} + \frac{2}{(1 - x)^2}.

    You need these terms to have the same denominator in order to add the numerators. To do this, multiply the first term by a cleverly disguised 1, in this case, \frac{1 - x}{1 - x}.

    So \frac{4}{1 - x} + \frac{2}{(1 - x)^2} = \frac{4}{1 - x}\times \frac{1 - x}{1 - x} + \frac{2}{(1 - x)^2}

     = \frac{4(1 - x)}{(1 - x)^2} + \frac{2}{(1 - x)^2}

     = \frac{4(1 - x) + 2}{(1 - x)^2}

     = \frac{4 - 4x + 2}{(1 - x)^2}

     = \frac{6 - 4x}{(1 - x)^2}.


    Also note that (1 - x)^2 = (1 - x)(1 - x) = -(x - 1)(1 - x) = -[-(x - 1)(x - 1)] = (x - 1)(x - 1).
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  3. #3
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    Smile

    That helps a lot,
    thank you very much
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