Thread: How to divide GCF through...

Hi and thanks in advance...

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

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

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!

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

$\displaystyle \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 $\displaystyle \displaystyle a^m \div a^n = a^{m-n}$

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

Finish him from here?

Originally Posted by kungfumonkey

Hi and thanks in advance...

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

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

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:
$\displaystyle \displaystyle 2x \sqrt{x^2 + 9} + \frac{x^3}{\sqrt{x^2 + 9}}$

Does this help?

-Dan

Thanks, you folks rule!

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

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