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Math Help - Simplify the following

  1. #1
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    Simplify the following

    1/square root of x^2 -4
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  2. #2
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    Quote Originally Posted by yess View Post
    1/square root of x^2 -4
    Do you mean \frac{1}{\sqrt{x^2}}-4 or \frac{1}{\sqrt{x^2-4}} ?

    I'll assume the first. Note that \sqrt{x^2}=|x|.
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  3. #3
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    sorry! its the second one you wrote =]
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  4. #4
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    Multiply it by \frac{\sqrt{x^2 - 4}}{\sqrt{x^2 - 4}}.
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  5. #5
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    Quote Originally Posted by yess View Post
    sorry! its the second one you wrote =]
    Well the radicand is not a perfect square.. so perhaps they want you to rationalize the denominator.
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  6. #6
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    so i worked it all out to 1/(x^2 - 4) is that right?
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  7. #7
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    No.

    What is \frac{1}{\sqrt{x^2 - 4}}\cdot \frac{\sqrt{x^2 - 4}}{\sqrt{x^2 - 4}}?
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  8. #8
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    Quote Originally Posted by Prove It View Post
    No.

    What is \frac{1}{\sqrt{x^2 - 4}}\cdot \frac{\sqrt{x^2 - 4}}{\sqrt{x^2 - 4}}?
    (√(x^2 - 4))/(x^2 - 4) ?
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  9. #9
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    Correct.
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  10. #10
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    so is that as far as it simplifies then??
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  11. #11
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    Quote Originally Posted by yess View Post
    so is that as far as it simplifies then??
    You can either write it as

    \frac{\sqrt{x^2 - 4}}{x^2 - 4} or \frac{\sqrt{(x-2)(x+2)}}{(x-2)(x+2)}, whichever you think is simpler...
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  12. #12
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    Quote Originally Posted by Prove It View Post
    You can either write it as

    \frac{\sqrt{x^2 - 4}}{x^2 - 4} or \frac{\sqrt{(x-2)(x+2)}}{(x-2)(x+2)}, whichever you think is simpler...
    ook so i just leave it the way it is like that? i squared top and bottom to get [(x-2)(x+2)/(x-2)(x+2)(x-2)(x+2)] so 1/(x^2 -4) but thats too far?
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  13. #13
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    \frac{\sqrt{x^2 - 4}}{x^2 - 4} \neq \left(\frac{\sqrt{x^2 - 4}}{x^2 - 4}\right)^2.
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  14. #14
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    Quote Originally Posted by yess View Post
    Simplify the following:

    1/square root of x^2 -4
    Where has the question come from? What is expected by "simplify"? Please give the broader context that the question comes from. There is insufficient information to know what sort of answer is expected.
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