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Math Help - Trouble understanding rewriting of an expression

  1. #1
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    Trouble understanding rewriting of an expression

    I'm trying to inverse a simple function but got stuck with some algebra I cant remember.

    I've got f (x) = 2x-1/x -1 and so far rewritten it to y(x-1) = 2x-1 but got stuck here. Reading the solution it show the next step as (y-2)x=y-1 but I'm at a loss trying to understand how they arrived here.
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  2. #2
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    Re: Trouble understanding rewriting of an expression

    Quote Originally Posted by dipsy34 View Post
    I'm trying to inverse a simple function but got stuck with some algebra I cant remember.

    I've got f (x) = 2x-1/x -1
    The first think you need to recall is the order of operations.
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  3. #3
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    Re: Trouble understanding rewriting of an expression

    Quote Originally Posted by dipsy34 View Post
    I'm trying to inverse a simple function but got stuck with some algebra I cant remember.

    I've got f (x) = 2x-1/x -1 and so far rewritten it to y(x-1) = 2x-1 but got stuck here. Reading the solution it show the next step as (y-2)x=y-1 but I'm at a loss trying to understand how they arrived here.
    I assume that you mean

    y=\frac{2x-1}{x-1} ............. If so:

    \begin{array}{rcl}y(x-1)&=&2x-1 \\ yx-y&=&2x-1 \\ 1-y&=& 2x-yx \\ 1-y&=&(2-y) x \\ \frac{1-y}{2-y}&=&x \end{array}
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  4. #4
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    Re: Trouble understanding rewriting of an expression

    Quote Originally Posted by earboth View Post
    I assume that you mean

    y=\frac{2x-1}{x-1} ............. If so:

    \begin{array}{rcl}y(x-1)&=&2x-1 \\ yx-y&=&2x-1 \\ 1-y&=& 2x-yx \\ 1-y&=&(2-y) x \\ \frac{1-y}{2-y}&=&x \end{array}
    Super, thanks.
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