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Math Help - Help with distributive property

  1. #1
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    Help with distributive property

    Hey I was doing a math problem and needed help with one certain part near the end of the problem. Here is the problem and what I have done already:

    8(1/x-7)=9(1/x)+3(1/5x)

    8/x-7=9/x+3/5x

    then I multiply each side by the least common denominator. I understand what to do on the left hand side, I just don't understand how to distribute the x-7 on the right (I assume the 5x gets canceled out:

    5x(x-7)*(8/x-7) = (9/x+3/5x)*5x(x-7)

    40x=(9/x+3)*(x-7)

    Any help would be greatly appreciated!!!! I'm really frustrated! I know the answer is 48x-336 but I can't see how to get there!
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  2. #2
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    PLEASE use brackets where they're needed or learn some LaTeX, it's impossible to tell if you mean \displaystyle \frac{1}{x - 7} or \displaystyle \frac{1}{x} - 7, or if you mean \displaystyle \frac{1}{5x} or \displaystyle \frac{1}{5}x.

    From your working, it looks like you meant

    \displaystyle \begin{align*}8\left(\frac{1}{x - 7} \right) &= 9\left(\frac{1}{x}\right) + 3\left(\frac{1}{5x}\right) \\ \frac{8}{x - 7} &= \frac{9}{x} + \frac{3}{5x} \\ \frac{8}{x - 7} &= \frac{45}{5x} + \frac{3}{5x} \\ \frac{8}{x - 7} &= \frac{48}{5x} \\ 8(5x) &= 48(x - 7) \\ 40x &= 48x - 336 \\ 336 &= 8x \\ 42 &= x \end{align*}
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  3. #3
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    Thank you, I understand it now... I see how it could be confusing, but you nailed it. I will try to figure out what LaTeX is.
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