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Math Help - How to divide GCF through...

  1. #1
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    Red face How to divide GCF through...

    Hi and thanks in advance...

    If I have this:
    % MathType!MTEF!2!1!+-<br />
% faaagaart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedm  vETj<br />
% 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpe  pC0x<br />
% bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq<br />
% pepae9pg0FirpepeKkFr0xfr-xfr-xb9Gqpi0dc9adbaqaaeGaciGa<br />
% aiaabeqaamaabaabaaGcbaGaaGOmaiaadIhacaGGOaGaamiEam  aaCa<br />
% aaleqabaGaaGOmaaaakiabgUcaRiaaiMdacaGGPaWaaWbaaSqa  beaa<br />
% caaIXaGaai4laiaaikdaaaGccqGHRaWkcaWG4bWaaWbaaSqabe  aaca<br />
% aIZaaaaOGaaiikaiaadIhadaahaaWcbeqaaiaaikdaaaGccqGH  RaWk<br />
% caaI5aGaaiykamaaCaaaleqabaGaaiylaiaaigdacaGGVaGaaG  Omaa<br />
% aaaaa!41E3!<br />
\[<br />
2x(x^2  + 9)^{1/2}  + x^3 (x^2  + 9)^{ - 1/2} <br />
\]<br />

    I understand that my GCF is :
    % MathType!MTEF!2!1!+-<br />
% faaagaart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedm  vETj<br />
% 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpe  pC0x<br />
% bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq<br />
% pepae9pg0FirpepeKkFr0xfr-xfr-xb9Gqpi0dc9adbaqaaeGaciGa<br />
% aiaabeqaamaabaabaaGcbaGaamiEaiaacIcacaWG4bWaaWbaaS  qabe<br />
% aacaaIYaaaaOGaey4kaSIaaGyoaiaacMcadaahaaWcbeqaaiab  gkHi<br />
% TiaaigdacaGGVaGaaGOmaaaaaaa!3741!<br />
\[<br />
x(x^2  + 9)^{ - 1/2} <br />
\]<br />

    What I don't understand is how to divide through by my GCF. What is throwing me off is that I don't know what to do with the -1/2 and 1/2 exponents... Can anybody please help me understand this? My professor is too fast and I'm the only idiot in the class! No other help is available to me until Monday and this is killing me! Thanks again, in advance for your time and help!
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  2. #2
    Master Of Puppets
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    \displaystyle 2x(x^2  + 9)^{1/2}  + x^3 (x^2  + 9)^{ - 1/2}

    \displaystyle \frac{2x(x^2  + 9)^{1/2}}{x(x^2  + 9)^{ - 1/2}}  + \frac{x^3 (x^2  + 9)^{ - 1/2}}{x(x^2  + 9)^{ - 1/2}}

    Using index law \displaystyle a^m \div a^n = a^{m-n}

    \displaystyle 2(x^2  + 9)^{1/2-(- 1/2)}  + x^2

    Finish him from here?
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by kungfumonkey View Post
    Hi and thanks in advance...

    If I have this:
    % MathType!MTEF!2!1!+-<br />
% faaagaart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedm  vETj<br />
% 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpe  pC0x<br />
% bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq<br />
% pepae9pg0FirpepeKkFr0xfr-xfr-xb9Gqpi0dc9adbaqaaeGaciGa<br />
% aiaabeqaamaabaabaaGcbaGaaGOmaiaadIhacaGGOaGaamiEam  aaCa<br />
% aaleqabaGaaGOmaaaakiabgUcaRiaaiMdacaGGPaWaaWbaaSqa  beaa<br />
% caaIXaGaai4laiaaikdaaaGccqGHRaWkcaWG4bWaaWbaaSqabe  aaca<br />
% aIZaaaaOGaaiikaiaadIhadaahaaWcbeqaaiaaikdaaaGccqGH  RaWk<br />
% caaI5aGaaiykamaaCaaaleqabaGaaiylaiaaigdacaGGVaGaaG  Omaa<br />
% aaaaa!41E3!<br />
\[<br />
2x(x^2  + 9)^{1/2}  + x^3 (x^2  + 9)^{ - 1/2} <br />
\]<br />

    I understand that my GCF is :
    % MathType!MTEF!2!1!+-<br />
% faaagaart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedm  vETj<br />
% 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpe  pC0x<br />
% bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq<br />
% pepae9pg0FirpepeKkFr0xfr-xfr-xb9Gqpi0dc9adbaqaaeGaciGa<br />
% aiaabeqaamaabaabaaGcbaGaamiEaiaacIcacaWG4bWaaWbaaS  qabe<br />
% aacaaIYaaaaOGaey4kaSIaaGyoaiaacMcadaahaaWcbeqaaiab  gkHi<br />
% TiaaigdacaGGVaGaaGOmaaaaaaa!3741!<br />
\[<br />
x(x^2  + 9)^{ - 1/2} <br />
\]<br />

    What I don't understand is how to divide through by my GCF. What is throwing me off is that I don't know what to do with the -1/2 and 1/2 exponents... Can anybody please help me understand this? My professor is too fast and I'm the only idiot in the class! No other help is available to me until Monday and this is killing me! Thanks again, in advance for your time and help!
    The 1/2 exponents are merely square roots. For example:
    \displaystyle 2x \sqrt{x^2  + 9} + \frac{x^3}{\sqrt{x^2  + 9}}

    Does this help?

    -Dan
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  4. #4
    Newbie
    Joined
    Apr 2011
    Posts
    6

    Thumbs up

    Thanks, you folks rule!

    I ended up with this thanks to your advice:
    % MathType!MTEF!2!1!+-<br />
% faaagaart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedm  vETj<br />
% 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpe  pC0x<br />
% bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq<br />
% pepae9pg0FirpepeKkFr0xfr-xfr-xb9Gqpi0dc9adbaqaaeGaciGa<br />
% aiaabeqaamaabaabaaGcbaWaaSaaaeaacaaIZaGaamiEaiaacI  caca<br />
% WG4bWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaGOnaiaacMca  aeaa<br />
% daGcaaqaaiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHRaWkca  aI5a<br />
% aaleqaaaaaaaa!3877!<br />
\[<br />
\frac{{3x(x^2  + 6)}}{{\sqrt {x^2  + 9} }}<br />
\]<br />

    And it seems that's the correct solution! THANK YOU SO MUCH!!!

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