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Math Help - sum of solutions?

  1. #1
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    Question sum of solutions?

    Solve:


    5/(x+4) = 4 + [3/(x-2)]

    What is the sum of your solutions?
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  2. #2
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    hey there sadieann

    the sum of your solutions is 6x + 10x - 4x squared..

    if you were to solve this you get x equal to 2.5 or -1

    hope that helps
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  3. #3
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    Quote Originally Posted by sadieann View Post
    Solve:


    5/(x+4) = 4 + [3/(x-2)]

    What is the sum of your solutions?
    Make a common denominator by multiplying all the denominators to make one. So (x+4)(1)(x-2) will give you a denominator of (x+4)(x-2)

    now you'll have
    (something)/(x+4)(x-2) = (something)/(x+4)(x-2) + (something)/(x+4)(x-2)

    to find out what that something is, make each term so that it denominator is this common one we just found.
    1) term 5/(x+4) ---> [5(x-2)]/[(x+4)(x-2)]
    2) term 4 ---> [4(x+4)(x-2)]/[(x+4)(x-2)]
    3) term 3/(x-2) ---> [3(x+4)]/(x+4)(x-2)]
    so now you have your terms, where their numerators can be added or subtracted with eachother since they all have like denominators.

    [5(x-2)]/[(x+4)(x-2)] = [4(x+4)(x-2) + 3(x+4)]/[(x+4)(x-2)]
    expand the numerator on each side. don't worry about the denominator since it's the same everywhere.

    so, 5x-10 = 4(x^2+4x-2x-8) + 3x+12
    5x-10 = 4x^2+16x-8x-32+3x+12
    5x-10 = 4x^2+11x-10

    So the question is... how do we make these two sides equal. Well, there's a number x which makes this possible. What's this number x? Let's find out. Bring all terms to one side, to start:
    0 = 4x^2+11x-10-5x+10
    0 = 4x^2+6x
    0 = 2x(2x+3)
    0 = 2x and 0 = 2x+3
    So x = 0 and x = -3/2

    There are two numbers that when substitued in for x, will make your original equation true.

    Did that help, because I'm not too sure what you were specifically asking.
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  4. #4
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    Yes! thanks a lot
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  5. #5
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    your welcome
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  6. #6
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    No problem!
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  7. #7
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    Sum of solutions.

    Quote Originally Posted by sadieann View Post
    Solve:


    5/(x+4) = 4 + [3/(x-2)]

    What is the sum of your solutions?
    The sum of the solutions is -1.5 or -3/2.

    LCM = (x+4)(x-2) , x not equal to -4; 2

    5(x-2) = 4(x+4)(x-2) + 3(x+4)
    5x-10 = 4(x^2 +2x-8)+3x+12
    0 = 4x^2 +8x-32+3x+12-5x+10
    0 = 4x^2 +6x-10
    0 = 2x^2 +3x-5
    0 = (2x+5)(x-1)

    x=-5/2 or x=1 (these are the solutions)

    the sum of the solutions
    = -5/2 + 1
    = -2.5 + 1
    = -1.5

    (I hope there aren't any mistakes...nice question. Cheers)
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