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Math Help - Solve equation for all real numbers a

  1. #1
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    Solve equation for all real numbers a

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  2. #2
    Super Member Quacky's Avatar
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    Re: Solve equation for all real numbers a

    Your first step is to put everything over a common denominator. Factor x^2-3x and see if you can work out what the common denominator is. Then, once you've done that, remember that the only way a fraction can be equal to 0 is if the numerator is equal to 0. This will give you an equation to solve for a.

    If you require further help, please show what you can do and we'll guide you from there.
    Last edited by Quacky; October 16th 2011 at 03:47 AM.
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  3. #3
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    Re: Solve equation for all real numbers a

    Okay, so x(x-3) is the common denominator. Which gives me (x^2 + ax-3a + x-12)/ x(x-3) =0 , or (x^2 + x(a+1) - 3(a+4))/ x(x-3).

    If I solve the numerator for x, I get x=3, and x=-a-4.

    Should I try to solve the equation first with x=3, and then x=-a-4?
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  4. #4
    Super Member Quacky's Avatar
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    Re: Solve equation for all real numbers a

    Quote Originally Posted by cristianodoni72 View Post
    Okay, so x(x-3) is the common denominator. Which gives me (x^2 + ax-3a + x-12)/ x(x-3) =0 , or (x^2 + x(a+1) - 3(a+4))/ x(x-3).

    If I solve the numerator for x, I get x=3, and x=-a-4.

    Should I try to solve the equation first with x=3, and then x=-a-4?
    Great work so far! You should notice quickly that x=3 cannot be a solution. Why?
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  5. #5
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    Re: Solve equation for all real numbers a

    Thanks! Yes, with x=3, the denominator is 0. So I put x=-a-4, which gives me the numerator 2a-4 and the denominator a^2 +11a+28.
    Do I solve the numerator for a now?
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  6. #6
    Super Member Quacky's Avatar
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    Re: Solve equation for all real numbers a

    Quote Originally Posted by cristianodoni72 View Post
    Thanks! Yes, with x=3, the denominator is 0. So I put x=-a-4, which gives me the numerator 2a-4 and the denominator a^2 +11a+28.
    Do I solve the numerator for a now?
    You're overcomplicating things and getting slightly muddled. We have learned that x=-a-4. Therefore, for all real values of a,

    a=-4-x

    We can't simplify any further.
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  7. #7
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    Re: Solve equation for all real numbers a

    Okay! Thanks for guiding me!
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