Math

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Solve for x.

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

Please show work!

  • Math -

    putting everything over a common denominator of (x-2)(x+2), we have

    x^2 = 5(x-2)
    x^2 - 5x + 10 = 0
    then just solve that for x

    Make sure that x ≠ ±2 since those values are not allowed in the original equation

  • Math -

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

    This calls for finding the common denominator, and then solving for x using the numerators.
    Do not forget to exclude the asymptotes values of x where the denominator becomes zero.

    LCM (lowest ommon multiple) of denominators (x-2), (4-x²) and (x+2) is (x²-4), since (x-2)(x+2)=(4-x²)

    Provided that x≠2 and x≠-2, then we can write the equation above as:

    [x(x+2)-2x]/(x²-4) = 5(x-2)/(x²-4)
    provided x≠2 and x≠-2

    Equating numerators,
    x²+2x-2x=5(x-2)
    =>
    x²-5x+10=0

    However, the solution does not have real roots. The complex roots are:
    x=(5±√*i)/2

  • Math -

    x=(5±(√15)*i)/2

    If you do not expect complex roots, please check for typos in the original question.

  • Math -

    Thank you guys! That is what I got. I wasn't expecting the complex roots.. That's why I wanted to check whether or not I was doing it right!

  • Math :) -

    You're welcome!

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