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Math Help - I need help beautifying this big ugly expression

  1. #1
    Junior Member
    Joined
    May 2008
    Posts
    45

    I need help beautifying this big ugly expression

    I'm stuck on how this question can go on:

    "The expression:
    \frac{\frac{1}{2x-1}+\frac{1}{y}}{\frac{x}{2xy-y}}
    is equivalent to..."
    I can flip the denominator of the whole fraction to multiply and factorize the y out but I can't seem to figure out a way to get past this:

    \frac{2x^2y-xy+4x^3-2x^3-2x-2x^2+1}{(2x^2-1)(x)}

    The answer to the question comes out as \frac{y+2x-1}{x}

    So I'm not sure how the first equation comes out as that ^
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  2. #2
    Junior Member
    Joined
    Jul 2009
    Posts
    44
    Quote Originally Posted by Kataangel View Post
    I'm stuck on how this question can go on:

    "The expression:
    \frac{\frac{1}{2x-1}+\frac{1}{y}}{\frac{x}{2xy-y}}
    is equivalent to..."
    I can flip the denominator of the whole fraction to multiply and factorize the y out but I can't seem to figure out a way to get past this:

    \frac{2x^2y-xy+4x^3-2x^3-2x-2x^2+1}{(2x^2-1)(x)}

    The answer to the question comes out as \frac{y+2x-1}{x}

    So I'm not sure how the first equation comes out as that ^
    Instead of flipping, multiplying, and doing all that other rather tedious stuff, we can do it much more easily:

    \frac{\frac{1}{2x-1}+\frac{1}{y}}{\frac{x}{2xy-y}}

    Let's get a common denominator in our numerator (god that sounds confusing):

    \frac{\frac{y}{2xy-y}+\frac{2x-1}{2xy-y}}{\frac{x}{2xy-y}}

    \frac{\frac{y+2x-1}{2xy-y}}{\frac{x}{2xy-y}}


    {\frac{y+2x-1}{2xy-y}} \cdot {\frac{2xy-y}{x}}


    {\frac{y+2x-1}{x}}
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