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Math Help - Solving Complex Fractional Equations

  1. #1
    Member purplec16's Avatar
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    Solving Complex Fractional Equations

    \frac{4m}{m-2}-\frac{13}{3m-6}=\frac{1}{3}

    I'm having problems finding a common denominator
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  2. #2
    Member mybrohshi5's Avatar
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    (4 m)/(m-2)-13/(m-6) = 1/3

    Multiply both sides by m-6:
    (4 (m-6) m)/(m-2)-13 = (m-6)/3

    Expand out terms on both sides:
    (4 m^2)/(m-2)-(24 m)/(m-2)-13 = m/3-2

    Write the left hand side as a single fraction:
    (4 m^2-37 m+26)/(m-2) = m/3-2

    Multiply both sides by m-2:
    4 m^2-37 m+26 = 1/3 (m-2) m-2 (m-2)

    Expand out terms on the right hand side:
    4 m^2-37 m+26 = m^2/3-(8 m)/3+4

    Subtract (m^2/3-(8 m)/3+4) from both sides:
    (11 m^2)/3-(103 m)/3+22 = 0

    Solve the quadratic equation by completing the square:

    Divide both sides by 11/3:
    m^2-(103 m)/11+6 = 0

    Subtract 6 from both sides:
    m^2-(103 m)/11 = -6

    Add 10609/484 to both sides:
    m^2-(103 m)/11+10609/484 = 7705/484

    Factor the left hand side:
    (m-103/22)^2 = 7705/484

    Take the square root of both sides:
    |m-103/22| = sqrt(7705)/22

    Eliminate the absolute value:
    m-103/22 = -sqrt(7705)/22 or m-103/22 = sqrt(7705)/22

    Add 103/22 to both sides:
    m = 1/22 (103-sqrt(7705)) or m-103/22 = sqrt(7705)/22

    Add 103/22 to both sides:
    m = 1/22 (103-sqrt(7705)) or m = 1/22 (103+sqrt(7705))
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  3. #3
    Member purplec16's Avatar
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    i dont understand it how u wrote it and the denominator was \frac{13}{3m-6}
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  4. #4
    Member mybrohshi5's Avatar
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    oops. that would have made it much easier haha.

    anyways m=1

    do you need the steps?
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  5. #5
    Member purplec16's Avatar
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    yes I'm trying to understand.
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  6. #6
    Member mybrohshi5's Avatar
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    factor out a 3 on the denominator of 3m-6

    so you will have 3(m-2) so to get common denominators just multiple the other denominator and numerator of 4m/(m-2) by 3.

    this will give you common denominators. can you solve for m from there?
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  7. #7
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    Quote Originally Posted by purplec16 View Post
    \frac{4m}{m-2}-\frac{13}{3m-6}=\frac{1}{3}

    I'm having problems finding a common denominator
    note that 3m-6 = 3(m-2)


    \frac{3 \cdot 4m}{3(m-2)}-\frac{13}{3(m-2)}=\frac{1(m-2)}{3(m-2)}

    denominators are all the same ... the numerator forms the equation

    12m - 13 = m-2

    solve for m , remember that m cannot equal 2.
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  8. #8
    Member purplec16's Avatar
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    i got the 12m-13 but i dont get how u got the m-2
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  9. #9
    Member purplec16's Avatar
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    would be willing to help me with a few other questions at least by telling me if you got the same answers?
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  10. #10
    Member mybrohshi5's Avatar
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     \frac{4m}{m-2}-\frac{13}{3m-6}=\frac{1}{3}

     \frac{3(4m)}{3(m-2)}-\frac{13}{3(m-2)}=\frac{1}{3}

     \frac{12m-13}{3(m-2)}=\frac{1}{3}

     \frac{12m-13}{m-2}=1

     12m-13 = m-2

    11m=11
    m=1
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  11. #11
    MHF Contributor
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    Quote Originally Posted by purplec16 View Post
    i got the 12m-13 but i dont get how u got the m-2
    look at the numerator on right side of the equation ...
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  12. #12
    Member mybrohshi5's Avatar
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    Quote Originally Posted by purplec16 View Post
    would be willing to help me with a few other questions at least by telling me if you got the same answers?

    i can help you for a little while =)
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  13. #13
    Member purplec16's Avatar
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    \frac{3}{2b+4}-\frac{4}{b-2}=\frac{3}{2b^2-8}
    is the answer to this 7 or am i wrong?
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  14. #14
    Member mybrohshi5's Avatar
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    do you understand it ok on how everything works out and how you get the m-2?
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  15. #15
    Member purplec16's Avatar
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    i understand how u got the m-2 on the left side on the equation but I dont understand what you did on the right
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