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Math Help - Review answer to simplification problem

  1. #1
    kkm
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    Review answer to simplification problem

    Given the following problem:

    \left(\frac{x^2-2x+1}{x^2+x}.\frac{2x+1}{x^2-x}\right)^{-1}+\frac{x^3-x}{(x+1)^2-x^2}

    Is my answer correct?

    = \left(\frac{(x-1)^2}{x(x+1)}.\frac{2x+1}{x(x-1)}\right)^{-1}+\frac{x(x+1)(x-1)}{(x+1-x)(x+1+x)}

    = \left(x-1\right)^{-1}+\frac{x(x+1)(x-1)}{(x+1-x)(x+1+x)}

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

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

    Answer:

    (x+1)^2

    I am not sure if that is correct, and would love someone to review my process, as I tried to be as detailed as possible.
    Last edited by kkm; June 25th 2012 at 05:43 PM.
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  2. #2
    MHF Contributor
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    Re: Review answer to simplification problem

    Sorry, but your process is VERY wrong.
    You are evidently unaware of the basics: you treat, as example, (a + b) / a as being equal to b.
    And x(x + 1) as being equal to (x + 1)^2.

    You need serious classroom help. This site isn't a classroom...
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  3. #3
    MHF Contributor
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    Re: Review answer to simplification problem

    Quote Originally Posted by kkm View Post
    Given the following problem:

    \left(\frac{x^2-2x+1}{x^2+x}.\frac{2x+1}{x^2-x}\right)^{-1}+\frac{x^3-x}{(x+1)^2-x^2}

    Is my answer correct?

    = \left(\frac{(x-1)^2}{x(x+1)}.\frac{2x+1}{x(x-1)}\right)^{-1}+\frac{x(x+1)(x-1)}{(x+1-x)(x+1+x)}

    = \left(x-1\right)^{-1}+\frac{x(x+1)(x-1)}{(x+1-x)(x+1+x)}

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

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

    Answer:

    (x+1)^2

    I am not sure if that is correct, and would love someone to review my process, as I tried to be as detailed as possible.
    To be of some more help, you should start by factorising as much as you can, to see if any factors can be cancelled.
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