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Math Help - How do I subtract and simplify this?

  1. #1
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    Unhappy How do I subtract and simplify this?

    Hi everyone, this is my first post and I don't really know how things work around here, but I'll ask my question.

    I'm in Algebra 2 and I'm having trouble finding how to do this particular problem in my textbook:

    Subtract, simplify, and note domain exclusion:

    (6/x^2-9)-(1/x-3)



    I know that I should probably factor the denominator of 6/x^2-9 because it's a difference of squares, but I have no idea how to make them both have like denominators in order to subtract! I also think that the exclusion is -3 but I'm not completely sure of that either.

    I know for a fact that the domain is (-∞, 3)∪(3,∞)

    Help as soon as possible would be greatly appreciated! (my test corrections are actually due tomorrow )



    -Lissy
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  2. #2
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    Quote Originally Posted by Numbers_Hurt View Post

    Subtract, simplify, and note domain exclusion:

    (6/x^2-9)-(1/x-3)



    I know that I should probably factor the denominator of 6/x^2-9 because it's a difference of squares, but I have no idea how to make them both have like denominators in order to subtract! I also think that the exclusion is -3 but I'm not completely sure of that either.

    I know for a fact that the domain is (-∞, 3)∪(3,∞)
    \frac{6}{(x+3)(x-3)} - \frac{1}{x-3}

    \frac{6}{(x+3)(x-3)} - \frac{x+3}{(x+3)(x-3)}

    \frac{6 - (x+3)}{(x+3)(x-3)}

    you finish


    btw, here is how to use parentheses properly to make your post clear ...

    6/(x^2-9) - 1/(x-3)

    also, I don't agree with your domain.
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  3. #3
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    Thanks for responding so quickly!

    can you cancel the x+3 so you are left with

    5/(x-3) ??

    and do you agree with the exclusions? I feel a bit stupid right about now.....
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  4. #4
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    Quote Originally Posted by Numbers_Hurt View Post
    Thanks for responding so quickly!

    can you cancel the x+3 so you are left with ... no, it's not a factor of the numerator

    5/(x-3) ??

    and do you agree with the exclusions? I feel a bit stupid right about now.....
    \frac{6 - (x+3)}{(x+3)(x-3)}

    \frac{3-x}{(x+3)(x-3)}

    -\frac{1}{x+3}
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