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Math Help - hard fraction

  1. #16
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    Not quite. What did you do with the (2) and the (3) to get its LCM? That's what you have to do with the (2) and the (x+2) in this situation.
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  2. #17
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    okay, would it be 2x+4?!?!?!?
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  3. #18
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    There you go. I'd probably write it as 2(x+2) to emphasize how you got it. Now that you know what the common denominator is, can you add the fractions together?
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  4. #19
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    YES!!!! so would the overall answer =x+9?
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  5. #20
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    No, I don't think so. Do this problem step-by-step. After you've found the common denominator, you add the fractions. What do you get when you do that?
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  6. #21
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    when i add them i get x-1-4 over 2x+4
    than i get X-5over 2x+4
    then, x-5=2x+4
    then, -5=x+4
    then, =x+9
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  7. #22
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    Aha. You're missing a very important step. Let's say you're adding the fractions

    \dfrac{1}{2}+\dfrac{1}{3}.

    We've already determined that the LCM of the denominators, which is the same thing as the common denominator, is 6. What would your next step be in this addition problem?
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  8. #23
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    1x1=1 and 2x3=6
    =1/6
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  9. #24
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    No, no, no. You've found the common denominator. Now you have to get the common denominator. You do that by multiplying fractions by fancy ways of writing 1 in order to obtain the common denominator in each denominator. Let me illustrate:

    \displaystyle \frac{1}{2}+\frac{1}{3}=\frac{1}{2}\left(\frac{3}{  3}\right)+\frac{1}{3}\left(\frac{2}{2}\right).

    So far, you would agree I haven't changed anything, right? I've multiplied each fraction by something that's equal to 1 (the fractions that are in parentheses). But I've chosen those numbers carefully so that when I multiply out the denominators, I'll get the common denominator that I need. Thus, the next step is to multiply out the fractions, which you can do the way you want to do it:

    \displaystyle\frac{1}{2}\left(\frac{3}{3}\right)+\  frac{1}{3}\left(\frac{2}{2}\right)=\frac{3}{6}+\fr  ac{2}{6}.

    Do you see how this is done? And do you know what the next steps are?
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  10. #25
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    yes i understand! after that would i add then and get 6/6=6?
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  11. #26
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    I'm not so sure you understand as well as you think you do. Yes, you would add, but the steps would look more like this:

    \dfrac{3}{6}+\dfrac{2}{6}=\dfrac{3+2}{6}=\dfrac{5}  {6}.

    Make sense? I think you multiplied instead of adding.
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  12. #27
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    oh i get it now
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  13. #28
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    Ok. So, picking back up from where we left off at post # 21, you're trying to add the two fractions

    \dfrac{x-1}{2}-\dfrac{4}{x+2}.

    You've determined that the least common denominator is 2(x+2). Now you have to get the common denominator. What do you get?
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  14. #29
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    now for my question, i have worked it out on a piece of paper and i get the answer as 2x^2 - 8x +12, would i then do quadratic equation to get the answer?
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  15. #30
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    I think you might be skipping steps there. That's not the quadratic that I get. Post your work, please.
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