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Math Help - Simplifying Fractions and solving for u

  1. #1
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    Simplifying Fractions and solving for u

    Could someone explain how to do this problem?

    Solve the following equation for u:
    Simplify your answer as much as possible.

    \frac{3}{u+3} =-5


    I couldn't find how to do this in my notes.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by eraser851 View Post
    Could someone explain how to do this problem?

    Solve the following equation for u:
    Simplify your answer as much as possible.

    \frac{3}{u+3} =-5


    I couldn't find how to do this in my notes.

    You want to clear the fractions by multiplying by the LCD in this case
    (u+3)

    So mulitiplying both sides by the above gives...


     (u+3) \cdot \frac{3}{u+3} =-5 \cdot (u+3)

    This gives a new equation without any fractions

    3=-5(u+3) \iff 3=-5u-15

    solving for u gives

    u=\frac{-18}{5}
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  3. #3
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    Quote Originally Posted by eraser851 View Post
    Could someone explain how to do this problem?

    Solve the following equation for u:
    Simplify your answer as much as possible.

    \frac{3}{u+3} =-5


    I couldn't find how to do this in my notes.
    \frac{3}{u+3} =-5

    Multiply both sides by u+3, the LCD

    \frac{3(u+3)}{u+3} =-5(u+3)

    3 =-5(u+3)

    3 =-5u-15

    Add 15 to both sides

    3+15 =-5u-15+15

    18 =-5u

    Divide both sides by -5

    u =\frac{-18}{5}
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  4. #4
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    Okay, I think I've got it now.

    I got a new problem with the same format. Could someone please check my answer to make sure I did it right?

    \frac{3}{x-1}=-2

    Multiplied both sides by (x-1)
    3=-2x-2
    Add 2 to both sides
    5=-2x
    And then divide both sides by -2.
    x=\frac{-5}{2}

    Did I do it right?
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  5. #5
    Behold, the power of SARDINES!
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    Quote Originally Posted by eraser851 View Post
    Okay, I think I've got it now.

    I got a new problem with the same format. Could someone please check my answer to make sure I did it right?

    \frac{3}{x-1}=-2

    Multiplied both sides by (x-1)
    3=-2x-2
    Add 2 to both sides
    5=-2x
    And then divide both sides by -2.
    x=\frac{-5}{2}

    Did I do it right?
    Not quite


    (x-1) \cdot \frac{3}{x-1}=-2(x-1)

    When the -2 is multiplied in you should get...

    3= -2x+2 \iff x=-\frac{1}{2}
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