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Math Help - Simplify ......

  1. #1
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    Simplify ......

    Simplify

    [(-16x^2+29x+6)-(16t^2+29t+6)]/x-t

    I noticed I can factor into (-x+2)(16x+3) etc..

    But, they are asking me to simplify. As far as I know, all this means is that I can simplify the top and get, [-16x^2+29x+16t^2-29t]/x-t. Do you think this is what they want? Or am I missing something?
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  2. #2
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    Re: Simplify ......

    Quote Originally Posted by StudentMCCS View Post
    Simplify

    [(-16x^2+29x+6)-(16t^2+29t+6)]/x-t

    I noticed I can factor into (-x+2)(16x+3) etc..

    But, they are asking me to simplify. As far as I know, all this means is that I can simplify the top and get, [-16x^2+29x+16t^2-29t]/x-t. Do you think this is what they want? Or am I missing something?
    OK first of all, I doubt you could have written the question correctly. Should the second lot of brackets start with -16t^2?
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  3. #3
    Super Member Quacky's Avatar
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    Re: Simplify ......

    Quote Originally Posted by StudentMCCS View Post
    Simplify

    [(-16x^2+29x+6)-(16t^2+29t+6)]/x-t

    I noticed I can factor into (-x+2)(16x+3) etc..

    But, they are asking me to simplify. As far as I know, all this means is that I can simplify the top and get, [-16x^2+29x+16t^2-29t]/x-t. Do you think this is what they want? Or am I missing something?
    Hey, great start. You're almost there. Once you're at this stage:

    \frac{(-16x^2+29x+16t^2-29t)}{x-t}

    Rewrite:

    \frac{(16t^2-16x^2+29x-29t)}{x-t}

    Partially factor:

    \frac{(16(t+x)(t-x))+29(x-t))}{x-t}

    Rewrite, changing the signs of the 16 and then second bracket (changing the 16 to -16 is the same as multiplying through by -1, changing the signs of the second bracket multiplies through by -1 again, so the end result is unchanged):

    \frac{(-16(t+x)(-t+x))+29(x-t))}{x-t}

    Rewrite again, just for clarity:


    \frac{(-16(t+x)(x-t))+29(x-t))}{x-t}

    And then we can cancel:

    -16(t+x)+29 (remembering that x\neq t)
    Last edited by Quacky; August 22nd 2011 at 07:30 PM.
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  4. #4
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    Re: Simplify ......

    Quote Originally Posted by Prove It View Post
    OK first of all, I doubt you could have written the question correctly. Should the second lot of brackets start with -16t^2?
    Yes, I am sorry for that. ....-(-16t^2...
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  5. #5
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    Re: Simplify ......

    Thanks!
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  6. #6
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    Re: Simplify ......

    Quote Originally Posted by StudentMCCS View Post
    Yes, I am sorry for that. ....-(-16t^2...
    Quacky's post shows the solution with the fixed sign
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