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Math Help - algebra 2 please help me!

  1. #1
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    Post algebra 2 please help me!

    2x / x^2 - 4

    +

    1 / x-2

    =

    2/ x+2

    Please solve and state if any solutions are extraneous! Thank you so much!
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  2. #2
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    Quote Originally Posted by gnarlycarly227 View Post
    2x / x^2 - 4

    +

    1 / x-2

    =

    2/ x+2

    Please solve and state if any solutions are extraneous! Thank you so much!
    2x(x+2)(x-2) + (x^2 - 4)(x+2) = 2(x-2)(x^2 - 4)

    2x(x^2 - 4) + (x+2)(x^2 - 4) - (2x - 4)(x^2 - 4) = 0

    (x+6)(x^2 - 4) = 0

    x = -6, x = -2 or x = 2

    Substitute them back into the original equation. Any answers which don't work are extraneous.
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by gnarlycarly227 View Post
    2x / x^2 - 4

    +

    1 / x-2

    =

    2/ x+2

    Please solve and state if any solutions are extraneous! Thank you so much!
    \frac{2x}{x^2-4}+\frac{1}{x-2}=\frac{2}{x+2}

    x^2-4=(x-2)(x+2)

    LCD=(x+2)(x-2)

    Multiply every term by the LCD and cancel where appropriate.

    2x+x+2=2x-4

    x+2=-4

    x=-6
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