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Math Help - Complex fraction help

  1. #1
    Junior Member
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    Complex fraction help

    If 0<x<y and x/y=r, which of the following must be equal to x+y/x?

    A
    B
    C
    D
    E

    The answer is r+1/r (D).

    I don't understand how they did this.
    I'm thinking it's because since x/y=r, if we moved the y over to the right, it'd be x=ry. So, in assuming that somehow y=1, then r multiplied by 1 would be r, thus x=r. And if x=r, then r would replace x in the fraction and 1 would replace y. But that doesn't make sense because why would y = 1? help. :P
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  2. #2
    A Plied Mathematician
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    You need to be more careful with parentheses. You have technically written x+(y/x), but I think you meant (x+y)/x. They are vastly different!

    Try breaking the fraction apart and see where that leads.
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  3. #3
    Senior Member eumyang's Avatar
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    Assuming that you mean \frac{x + y}{x}:

    \begin{aligned}<br />
\frac{x + y}{x} &= \frac{x}{x} + \frac{y}{x} \\<br />
&= 1 + \frac{1}{r} \\<br />
&= \frac{r}{r} + \frac{1}{r} \\<br />
&= \frac{r + 1}{r}<br />
\end{aligned}
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  4. #4
    Junior Member
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    Quote Originally Posted by eumyang View Post
    Assuming that you mean \frac{x + y}{x}:

    \begin{aligned}<br />
\frac{x + y}{x} &= \frac{x}{x} + \frac{y}{x} \\<br />
&= 1 + \frac{1}{r} \\<br />
&= \frac{r}{r} + \frac{1}{r} \\<br />
&= \frac{r + 1}{r}<br />
\end{aligned}
    Thank you! Also, I'll try to be more careful with my parenthesis Ackbeet. This isn't the first time you've told me iirc. :P
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