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Proving a equation - im stuck

  1. Jun 2, 2007 #1
    1. The problem statement, all variables and given/known data
    2. Relevant equations
    Show that the equation

    [tex]\frac{2}{x+1}+\frac{1}{x+2} = \frac{1}{2}[/tex]

    can be written as [tex]x^{2} + x - 4 = 0 [/tex]

    3. The attempt at a solution

    mulitply the fractions on the LHS numerators by opposite denominators and multiply denominators togethter giving me:

    [tex] \frac{3x + 5}{x^{2} + 3x + 2} = \frac{1}{2}[/tex]

    cross multiply

    [tex]x^{2} + 3x + 2 = 6x + 10[/tex]
    which is rearanged to give [tex]x^{2} - 3x - 8 = 0 [/tex]

    which is wrong :(

    Where have I gone wrong
  2. jcsd
  3. Jun 2, 2007 #2
    Try to guess if the statement is right... for example using the roots of the second equation in the first equation.
  4. Jun 2, 2007 #3
    indeed, your working is correct.

    the question stated is obviously incorrect ...

    When you place the roots found from your equation [tex]x^{2} - 3x - 8 = 0 [/tex] as Coren said back into the equation, the solution is 1/2

  5. Jun 2, 2007 #4


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    Homework Helper

    Nope, it's totally correct. The answer the book gives is wrong.
    So, congratulations. :)
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